It’s tourist season in a small Cornish fishing village, and though lifeboatman Steve Kellow has his hands full dealing with his job and his sullen teenage sister Nina, he still finds time to chat up a raven-haired young woman who wants to know about the tide. However, the woman and her equally dark-haired male companion are breaking the rules by being here, and they learn the consequences of their actions too late when the man suffers a terrible accident while exploring the sea late at night. Some time afterwards, Steve and his crew are called out to recover a body found floating in the sea, an unidentified man with jet-black hair. The body is taken to the morgue for a post-mortem, and soon afterwards rumours begin to circulate in the village that it was found to be surgically altered somehow. Meanwhile, the woman, nearly paralyzed with grief, tries to pull herself together and dyes her hair to disguise herself, hoping to find what she needs to get back home...
Local fisherman Charlie Johns calls on Steve and his crew to help out when one of his crab pots gets snarled on something on the sea bed. On a quiet day, Steve dives to investigate and finds the crab pot caught on some unidentifiable, twisted metal wreckage. While pulling the crab pot out he finds an odd cylinder of metal, the size and shape of a cigarette lighter, and gives it to Charlie as a souvenir. Charlie plans to make a pendant out of it, and although Steve later notes that he’s developed a rash on his hands, it clears up soon afterwards and he fails to draw any connection to the strange metal object.
While sunbathing on the beach, Nina encounters an eccentric long-haired stranger who offers her a jelly baby, and a beautiful red-haired woman who claims to be reporting on the discovery of the unidentified body. Somewhat maliciously, Nina sends her to Steve, hoping that her brother will treat the reporter with the contempt she deserves. However, Steve is instantly infatuated with her and agrees to tell her about the body. He’s amused when she calls herself Redruth; this is the name of a local town, but fortunately for her, he assumes it’s a nickname for Ruth. She’s also fortunate in that Steve is too captivated by her to really notice she isn’t taking any notes during her interview, or that she has nothing to drink while they are talking in the local restaurant. Nina is suspicious of Ruth, but Steve, believing she’s just jealous, doesn’t listen to her claims that Ruth is behaving strangely.
Charlie Johns apparently comes down with the flu, and although Steve means to check in on him, he leaves it too late and Charlie suffers a fatal heart attack. He leaves Steve the pendant he made of his “souvenir,” and Steve, feeling guilty, promises to wear it as a reminder. Over the next few days, Steve continues to see Ruth on and off, but Nina wonders why Ruth is staying in the village for no apparent reason, and notes that Steve is beginning to look pale and wan. When Ruth attends Charlie’s funeral with Steve, Nina notes that she too looks ill -- and sees the eccentric stranger from the beach sitting nearby, watching Ruth. Ruth makes an excuse not to leave the church until it’s stopped raining, and Nina, suspicious, follows her but loses her near the cliffs. What she doesn’t know yet is that Ruth is sicker than she looks -- in fact, she’s dying.
Nina is convinced that there’s a link between Ruth’s behaviour and her brother’s ill health, but Steve dismisses her groundless accusations as jealousy. Unable to find out where Ruth is staying, Nina decides to follow the long-haired stranger, believing that he is also following Ruth for some reason. She tracks him down to a guest cottage, where she sees a police box sitting in the living room and is confronted by the stranger, who identifies himself as “the Doctor” and offers to share his story with her. Suspicious, she refuses to enter his cottage, but accepts his invitation to the local bistro, where she listens in amazement as he casually explains that Ruth is from another world, and that he’s come to find out why she’s here and whether she is responsible for the recent deaths.
Nina refuses to accept the Doctor’s weird story without proof, and he therefore invites her to return to his cottage tomorrow when it’s light and see his TARDIS for herself. She is still uncertain, but accepts the invitation -- and bursts into tears when he opens up the police box to reveal an impossibly huge interior. Everything he told her was true. Nina recovers and tells her story to the Doctor, who deduces that the drowned man and the weird pendant may be the key to solving the mystery. Nina thus bypasses Steve’s suspicious roommate, steals the pendant from his dresser and gives it to the Doctor so he can run tests on it.
As Nina waits for the Doctor to finish his work, she catches sight of Ruth near the cliffs and realises from her shambling gait that there’s something wrong. She loses sight of Ruth again, but by this time the Doctor has found out what the metal cylinder is and has identified Ruth’s planet of origin. Her people are peaceful travellers with strict rules about non-interference in other cultures, and the Doctor suspects that Ruth and her dead companion were young rebels breaking the rules. Their thrill-seeking has already resulted in tragedy, as water is deadly to Ruth’s people; the Doctor must find her before her genetic disguise wears away completely and the atmosphere of Earth kills her as well.
Steve returns home to find that Ruth has cancelled their date on another flimsy excuse, and when he finds that Nina has stolen his pendant he loses his temper completely. His friends have seen Nina in the Doctor’s company, and Steve catches up with them on the cliffs, where they are searching vainly for any trace of Ruth’s bio-signs. Furious, Steve accuses the Doctor of cradle-robbing and demands that he return the pendant. Fearing that the Doctor will do so, and realising that it’s the pendant which is killing her brother, Nina impulsively grabs the pendant from the Doctor and throws it over the cliff. Enraged, Steve takes her back home, as Nina realises from the Doctor’s horrified reaction that she’s made a terrible mistake.
Steve doesn’t believe Nina’s wild claims about aliens, and she knows that he and his friends will be watching her closely to ensure that she doesn’t try to meet the Doctor again. However, Nina works out on her own that the Doctor’s bio-sensor was unable to locate Ruth because she was shielded by the minerals in the sea caves which riddle the cliffs. Nina enters the tunnels to investigate, and manages to track Ruth down -- but Ruth is dying, ill and frightened, and she doesn’t listen when Nina insists that her friend the Doctor just wants to help her. Ruth blames herself for breaking the rules and getting her lover killed, and fears that even if she could return home, nobody would forgive her for what she’s done. As Ruth flees deeper into the caves to die next to the gateway home, the horrified Nina realises that the pendant she threw into the sea was the key to Ruth’s only way home; she’d been looking for it all along without ever realising that Steve had it, and now it’s lost forever.
Nina tries to follow Ruth, but a piercing electronic whine from the gateway resonates through the tunnels and causes the roof to cave in. Nina barely gets out as the mines collapse behind her, sealing Ruth off. Nina goes straight to the Doctor, but due to interference from the same mineral deposits that shielded Ruth from his sensors he’s unable to pilot the TARDIS directly to the gateway. He decides to risk climbing down the cliff to get into the mines through the sea caves, but the weather turns rough and he’s trapped when waves begin to lash the cliff. Nina phones in an anonymous tip to the lifeboat station, gets there first and dons one of the dry suits, disguising herself as one of Steve’s crewmen. By the time Steve realises what she’s done the boat is already on its way, and when she tells him that Ruth is in danger, he decides to continue on with the rescue, taking Nina along although this means breaking all of the Royal National Lifeboat Institution’s safety procedures.
The lifeboat reaches Derry’s Head, where the Doctor leaps from the cliff onto the boat -- and before Steve can stop him, the Doctor takes the till and pilots the boat into the cave he was trying to reach. They have only an hour to rescue Ruth before the tide rises too high for them to get out of the cave. Steve accompanies the Doctor and Nina, but is stunned when they enter a large cavern with a flickering dimensional gateway in the centre. Ruth is lying comatose nearby, and her disguise has decayed even further to the point where it’s obvious she isn’t remotely human. Stunned, Steve nevertheless helps the Doctor to wrap up Ruth in Nina’s dry suit, shielding her from the sight of the lifeboat’s other crewman.
Steve pilots the lifeboat back to the pier, where the angry Ops Manager is waiting for them. The Doctor uses light hypnosis to get past the waiting paramedics and carry Ruth to the TARDIS, but Nina takes responsibility for what she’s done to Steve and stays at the pier to ensure that her actions don’t cost him his job. By the time she gets to the cottage, the Doctor has gone, but some time later, he returns, bringing Ruth’s parents to thank Nina and Steve for helping their daughter. Ruth herself is recovering back in her own world, and Nina’s happy to learn that she will not be punished any further for what happened. The Doctor bids Nina a proper goodbye this time, and promises one day to return.