The date is the 20th of October, 1901. As the cargo ship Lankester fights it was through an ocean storm midway between Madagascar to New Orleans, its bell rings relentlessly in the wind. Chief Mate Jacques De Requin believes this is the worst storm they have every experienced, not quite a hurricane but blowing at least 55 to 60 miles an hour. They’ve had to endure this for four days now and they’re wondering if it’s ever going to let up. Captain Callany assures them they have a sturdy vessel and they’ve survived much worse than this. He’s proud of the fact that the Merchant Board has never fined him yet for late delivery of his cargo. Crewman McTigh returns from the hold where he was checking the cargo and assumes his duties in the wheelhouse, while Callany and De Requin decide to ride out the storm below deck. De Requin has been with Callany for nearly three years and he’s been a Chief Mate even longer than that, yet he’s never applied for a ship of his own. He says he’s not ready for such a position, but his Captain wonders whether his friend’s views would change if he were to retire. He’s not planning to do so just yet, but he knows he’s not as young as he once was and he’s not sure that an old sailor like him fits in with the modern Merchant Navy. Although De Requin believes his own career may take a different route but Callany reminds him that he owns the Lankester and what happens to her is his responsibility, not the Navy’s. When he does decide to retire, it is his intention to hand it over to his Chief Mate.
At the dining table, the Doctor finishes a laborious joke about Livingstone, an elephant and a gorilla suit - which fails to meet with the expected approval of his fellow guests. The Captain and Chief Mate joins them as the Doctor is admonishing the crew for being such a miserable lot. The storm is obviously affecting everyone, but Callany hopes it may start relenting in a few hours. Peri asks how their fellow passenger Amy Ivens is doing and whether she’s going to be coming out of her cabin, but De Requin says that unfortunately she is still unwell and will need to remain alone for the duration of the voyage. As Dr Blackwell has ‘disappeared‘, the Doctor offers to look in on her, but the Chief Mate says that won’t be necessary as he’s been given the medication she needs and Miss Ivens, who is self-conscious about being in a wheelchair, gets worried when strangers attend to her. Peri and the Doctor argue that they’re hardly strangers and have been aboard ship long enough now to be acquainted with everyone, but Dr Blackwell’s diagnosis was solitude and Callany feels that decision should be honoured. De Requin has some personal tasks to attend to and makes his excuses from the table. The Doctor asks for permission to place his ’crate’ below deck, and although the cargo hold is already cramped, the Captain agrees to see what he can do. Apart from the weather, the Doctor claims to be having a most enjoyable trip, but Peri hasn’t acclimatised to the permanent smell of fish yet. Their conversation is suddenly interrupted by a blood-curdling scream from the deck…
They race up to the deck and find one of the crewmen, Crawford, lying dead in a pool of blood. De Requin is already there, but says he didn’t see anything. The Doctor discovers the man has been stabbed, more than once. After Dr Blackwell, Crawford is now the second person to die on this voyage, and although there is no indication that the two men died the same way, the obvious conclusion is that someone on board intends to wipe them out one by one. Callany is disturbed by the Doctor’s suggestion that one of his crew may be responsible, but whoever did it must have left in a hurry as the Doctor finds the dropped murder weapon. Unless the attacker jumped overboard in the middle of the storm, they can‘t have gone far. De Requin wants to search the ship and advises the others to join Amy in her cabin for their own safety, but the Captain will only allow Peri to leave. Pointing to the knife in the Doctor’s hands, Callany places him under arrest for murder. The time travellers are outraged, but the Doctor’s argument that he was with them below deck when they heard the victim scream falls on deaf ears. Despite his protests, the Doctor is placed under court martial and escorted to the brig.
Peri bemoans the fact that fate always seems to land them in the middle of a crisis. This was supposed to have been a couple of relaxing weeks on board a luxury liner heading to far and distant lands. Instead, here they are on a cramped steamship in the middle of a storm, accused of murder. The Doctor concedes that even his cell could do with a bit of a clean. The good news is that the TARDIS is now safely stowed away in the cargo hold, as the salt water was starting to eat away at the outer shell. The Doctor is curious about the murder weapon which appeared to be formed from coral, although it felt heavy as though its density had been altered. He admits his marine biology is a bit rusty and wonders if Peri could get it for him so he can examine it more closely. She’s suspicious of the way De Requin seems to stay close to Amy all the time, but the Doctor reminds her that she’s unable to move from her cabin so the Chief Mate has taken responsibility for looking after her. Peri wishes they’d stayed in Madagascar and the Doctor promises that when this is all over, they can go back there.
The Captain and Chief Mate examine the murder weapon in more detail but don’t know what to make of it. As Peri joins them, instructions are being given for the top mast to be cut away to prevent it cracking down through the decking should the ship flounder. De Requin points out that without the mast, the ship won’t have any means of propulsion if the engines flood. Peri protests the Doctor’s innocence, but Callany refuses to listen. Peri and De Requin remind him that as the Doctor is neither a sailor nor a member of the crew, he can’t be handed over to a court martial. However, Callany argues that as a medical professional, the Doctor can be drafted under emergency powers that allow a ship’s Captain to make immediate additions to the crew. For the remainder of the journey, the Doctor will be assigned to look after Amy’s medical needs, and if he tries to escape he will be shot as a mutineer. When they reach New Orleans, he can be dismissed from service, but will remain in the employ of the Merchant Navy and can therefore be sent for court martial.
As the Doctor is released from his cell, he asks Peri to remind him never to ask for her help again. For the next two weeks his every move will be monitored by crewman McTigh. Amy has taken a turn for the worse during the night, so the Doctor is asked to make his first visit straight away. They find her asleep and De Requin tells them Amy frequently drifts in and out of consciousness. The Chief Mate revives Amy with smelling salts and then leaves, taking McTigh with him. The Doctor decides his first course of action is to find out exactly what is wrong with his patient. Her skin is pale and clammy and he asks Peri to force open the jammed porthole to allow more air inside. As she does so, she notices the outside of the frame is scratched as if something had been trying to claw it open. The Doctor begins to suspect that Amy has been drugged. The young woman wakes up but her vision is blurred and Peri notices there are cataracts in her eyes. The Doctor realises they are actually inner eyelids. He asks her about her strange wheelchair, which completely encases her legs, but she tries to avoid answering any direct questions about her condition. Suddenly an unearthly face appears at the porthole, but it disappears before anyone can get a closer look. The Doctor can’t help feeling that although they are alone in the middle of the ocean, the crew is being watched…
Secretly, De Requin is making radio contact with someone using the call sign ‘Open Water’, but the intensity of the storm is preventing his messages from getting through. He tells his contact that the weather is worsening but the cargo remains intact. The problem with the ship’s doctor has been resolved and the Captain has drafted the services of a civilian scientist who’s providing medical attention to the cargo now. He’s about to discuss delivery to their client when he is interrupted by the Doctor who enters the hold looking for supplies. The Captain arrives and asks the Doctor why he is travelling to New Orleans on this particular ship. He isn’t convinced by the explanation that the Lankester just happened to be going in the same direction and he believes the Doctor knows more than he is saying. The Captain has come to realise they are not alone on this ship - something else is with them and has been aboard ever since they left Nosy Barren. He fears for the safety of himself and his crew and believes they are being picked off one by one. When he expressed his concerns to his Chief Mate earlier, he was dismissed as one of the “old school of mariners”, wallowing in superstition and senility. He is now suspicious of De Requin and arranged for the Doctor to be falsely accused on trumped up charges so that he could talk to him without alerting his Chief Mate. He doesn’t actually believe De Requin is the murderer, but he’s sure that he’s somehow connected to the deaths.
The ship suddenly jolts and, despite the fact that they’re in the middle of the ocean, Callany believes they have run aground! Amy and Peri also wonder whether they’ve hit some rocks. Amy is concerned that the Doctor has not yet returned and Peri admits that they think the young woman is being poisoned. In the hold, the Doctor explains to Callany that Amy has been deliberately given small doses of mercury - the perfect cover as it‘s a common form of poisoning among fishermen and merchant sailors due to the high levels of mercury in fish. Somebody doesn’t want her dead, but sick - possibly to keep her out of the way for some reason. De Requin returns to Amy’s cabin and tells them the Doctor asked him to administer a relaxant. Amy protests she is too weak to take any more - but the Chief Mate reveals this sample isn’t for her, it’s for Peri. It’s neat mercury and she’ll be dead within minutes! They struggle and Amy promises De Requin that she won’t tell her secret to Peri. She knows he can’t harm her for fear of losing out on his fortune. Suddenly the ship jolts again and Amy is knocked out of her wheelchair. It was filled with water and the secret is finally revealed - Amy is a mermaid!
The Captain realises that the hull of the ship has been breached. They may have a day left before they sink, or they may just have an hour. There’s no way of telling until they’ve examined the damage, but it will be suicide to go down to the hold. Nevertheless, the Doctor insists on going as he has some ‘equipment’ down there that he needs to retrieve. Callany receives a message from McTigh telling him that the ship is taking on water fast. He goes to the wheelhouse to switch on the pumps in order to give them as much time as possible to evacuate the ship, although Callany has no intention of leaving himself as a Captain never abandons his ship.
The Chief Mate almost wishes he’d let the mermaid die in the fishing nets for all the trouble she’s caused him, but he still plans to sell her as he’ll earn enough money to set him up for life. He has no desire to see out the rest of his days smelling of fish. When De Requin leaves, Peri tries to help Amy who is now weakening as she’s exposed to the elements. She cannot believe that someone as beautiful as Amy is going to die in such a pointless way. She and the Doctor have seen so many races and so many cultures that sometimes she takes things for granted and doesn’t embrace it as she should. Amy explains that some of her people have the ability to walk on land, but it takes a lot of strength. To her, the land is the ocean floor - a desert of brimstone that they float above while bathing in its warmth. There are colours and shapes that most people can only dream of, and the trees and plants move in the slightest current. Their homes are made of coral with roofs of mussel shell that open and close with the flow of the water. The pearls inside glisten and sparkle, and when there is dead calm on the surface, the yellow sun brings them alive. Peri asks how she ended up on the ship and Amy explains that one day some of them were fishing near the coast when her daughter Galatea caught her tail in the nets and they were both captured when she went to rescue the baby. Galatea is also on board the ship, imprisoned in a tank hidden behind a panel on the wall which De Requin installed.
Captain Callany goes to the cargo hold and finds the Doctor already there examining the hull breach. Despite his determination to reach New Orleans, it’s obvious to both of them that the ship cannot be saved. Callany wonders what would have the strength to cause so much damage, especially when the Doctor observes that the torn metal has been peeled back. The Doctor asks about their strange passenger and the Captain explains that Amy is an acquaintance of De Requin who came aboard when they docked at Nosy Barren. Suddenly the Doctor sees something moving in the water, like a big fish. He then realises that the TARDIS is missing - it must have fallen through the hole and is probably now at the bottom of the ocean! The Doctor decides they have no choice now but to abandon ship, but he must find Peri first. He suddenly cries out and disappears into the darkness. Callany calls out for him, but there is no reply.
Amy asks Peri to promise that no matter what happens to her, she will make sure her daughter is safe. Peri assures her that the Doctor can take them both home before De Requin reveals their existence to the rest of the world, but Amy believes this will just force the Chief Mate to return later to search for more of her people. She starts to panic and has trouble breathing. Peri is unable to save the life of her friend and swears vengeance on De Requin. She bangs on the door, demanding to be released.
The Chief Mate once again tries to make radio contact with ‘Open Water’ and begs them to send a rescue ship. Before he can get a reply, Peri bursts in and confronts him. She accuses him of murdering the rest of the crew, but all he is interested in is getting his hands on the mermaid baby. He points out that she cannot simply return the baby to the sea as it’s less than a week old and couldn’t possibly survive on its own. Only by giving Galatea to him will she live. If she won’t, then he will shoot them both…
Captain Callany makes his final ever entry in the Lankester’s log. He describes how an unknown force struck the ship two days out from the Cape of Good Hope. The ship’s instruments can no longer record their position, but he hopes the log will one day be found so that the necessary announcements regarding their loss can be properly issued.
The Doctor wakes up and hears a voice telling him he is safe. He finds himself in an underwater cave on the sea bed, surrounded by hundreds of mermen. The voice belongs to Nerus, who tells him their species is endangered and that two of their kind are being held on the ship - including Anthratrite, the mermaid known as Amy. The Doctor never ceases to be amazed by this planet. No matter where he goes, the variation of life it produces astounds him. He admits that even he thought merpeople were a myth! Nerus is Anthratrite’s father and grandfather to Galatea. He asks for help in finding them, but the Doctor believes this may be impossible as the ship has probably sunk already by now. Although he cannot help the merpeople, he instead asks for their help in rescuing Peri, which infuriates Nerus. The Doctor can understand their reluctance - if they reveal themselves to the survivors of the ship it could bring others to search them out. He agrees that they should remain below the sea and hide from man or they’ll be hunted to extinction. However, Peri is entitled to a wonderful future, so he must try to find a way to help her alone, even though he knows he doesn‘t have the lung capacity to survive the swim to the surface. Nerus is surprised that they’re prepared to give up their lives to protect the merpeople. He tells the Doctor he was the one watching them through the porthole on the Lankester and he arranged for both the Doctor and his ‘equipment’ to be brought down. Nerus also reveals he was the one who killed Dr Crawford, and although he claims he did it to protect their world, the Doctor refuses to condone murder, no matter what the provocation. In return for giving him back the TARDIS, Nerus asks to be taken to his daughter and he demonstrates his ability to transform his own body, changing his tail into human-like legs.
De Requin forces Peri and Galatea into the Lankester wheelhouse and confronts Captain Callany at gunpoint. He accuses the Captain of keeping him in his shadow all these years, smothering him into thinking the same way he does. He’s not willing to continue down this path and he demands a lifeboat. Peri tells Callany that everything De Requin did was just for money and she reveals that Amy was a mermaid. He finds this difficult to believe until she shows him the baby. He offers his Chief Mate the ship and tells him he can sell it if money is all that he wants, but he won’t give him access to a lifeboat. The Captain reveals that McTigh and the other surviving crewmembers are already taking the only remaining lifeboat, so threatening to shoot them will make no difference. He accuses De Requin of causing the deaths of Crawford, Blackwell and the Doctor, if not directly then as a result of his actions. Peri becomes distraught when the Chief Mate finally snaps and shoots his Captain dead.
De Requin leads Peri and Galatea out onto the deck, and when they see the crew jumping into the sea they realise the ship is beyond saving. Suddenly the TARDIS materialises and the Doctor introduces Peri to Nerus. De Requin threatens to shoot everyone, and Nerus realises he was the evil that descended on his people. He reveals he is Anthratrite’s father and the increasingly unstable Chief Mate is shocked to learn that he is also a merman. There is a stand-off between the two until the Doctor points out that they don’t have long left before the Lankester finally sinks into the Atlantic. De Requin sees hundreds of the merpeople below the surface and he demands they surrender to him so he can breed more of them for captivity in his own zoo. He starts to become demented, laughing maniacally at his own plans and ignoring the pleas of those around him. The Doctor refuses to allow him to create his own freak show and turn the merpeople into a circus attraction. When Peri reveals that he has already killed Amy, Nerus agrees to give De Requin what he wants - but not in the way that he expects. He will get to see as many of his people as he likes…at the bottom of the ocean. Nerus starts to transform back into his merman form and De Requin finally snaps, becoming completely insane. Nerus announces that the sailor will become their circus attraction and the merpeople surround him and drag him screaming under the sea.
As the ship sinks below the surface, the Doctor, Peri and the baby escape in the TARDIS. It materialises in the underwater cave and they hand Galatea back to her own people, confident that she will grow strong now she is with her own kind. Peri is completely exhausted. She thought that merpeople were supposed to be placid, but the Doctor now knows this is only true in the world according to Hans Christian Anderson. They meet Nerus, who is delighted to welcome back his granddaughter. He is grateful to them and Peri asks a favour in return. She asks the merpeople to save the sailors who jumped overboard, but when he refuses as the risk of exposure to the world is too great, she argues that any of them who are still alive will be half-drowned, so they could be taken to a nearby island. If any of them mention seeing merpeople, they will be thought of as delirious. The Doctor agrees it is a big risk, but it might be the right thing to do. Nerus is sympathetic to Peri after she saved Galatea and eventually he agrees to her plan. The Doctor and Peri make their final goodbyes and leave in the TARDIS.