London, March 1702. Something devilish is stalking the streets of London, but in the Diabola Club young libertines continue to amuse themselves as usual, gambling, dining and gossiping about the recent death of the King. When Edmund Carteret's losses and the taunting of his friends Quincy Flowers and Jasper Jeake become too much, he storms off, claiming that he wants something more adventurous out of life than their company. His comment is overheard by Sir Nikolas Valentine, a solitary player who claims to be playing a game of his own devising, and who invites Carteret to his table. There are those who claim that Valentine is in league with the devil himself, and Carteret, intrigued by Valentine's reputation, sits down to play...

The Doctor tries to teach Turlough how to play cricket, but Turlough is bored and confused by the overly complex rules, and the Doctor gives him a copy of the 1928 edition of Wisdon's Almanac to consult. The TARDIS materializes in the sitting room of Dr Samuel Holywell, shortly after Holywell has dismissed his maid Hannah and retired for the night. The Doctor and Turlough emerge to explore, and find evidence that their unwitting host is a collector of the unusual. When Holywell investigates the noise and catches them, the Doctor claims to have been delivering a package to him -- an odd "police box" from the New World. Holywell is still suspicious until the Doctor charms him into talking about his collection, which he does with enthusiasm once he realizes that the Doctor is a fellow collector. As Holywell shows the Doctor about, Turlough looks around for something to eat, and finds evidence that Holywell's interests have led him to the study of dark magic.

Sir Nikolas Valentine departs from the Diabola Club, but before going he invites the servant Poltrot to play at cards with him the next night; he has heard that Poltrot used to be a schoolmaster before the love of ale ruined him, and he claims that he may be able to help. Flowers, looking for the missing Carteret, questions Poltrot and learns that Carteret left in a daze some time ago after playing cards with Valentine. Flowers and Jeake depart, pondering the odd behaviour of their friend and wondering if the strange Valentine has some sort of hold over him. Their discussion is interrupted by a masked highwayman who relieves them of their purses, but their outrage becomes delight when the departing robber identifies himself as Major Billy Lovemore; they've just been robbed by the most notorious highwayman in London, and they'll dine out on the story for years to come. Elsewhere, two alien creatures discuss the progress of their client's mission; most of the primitive city has been searched, but there is still no sign of the target...

Carteret collapses in the street, and the demonic sounds stop immediately. As Cotton flees in terror, the Doctor examines Carteret and finds that his heart has given out from sheer fright -- and clutched in the dead man's hand is a single playing card, the Ace of Hearts. The Doctor places the card in his copy of Wisdon's Almanac for safekeeping, while Holywell comforts the distraught Hannah and fears that his researches may have conjured up the Devil. Holywell and Hannah take the body indoors while the Doctor sets off in search of Turlough; he is unable to locate him, but Holywell offers to let the Doctor stay with him until his friend is found again. Elsewhere, the disappointed Valentine urges the screaming voices about him to rest easy; in just a little while, all their work will be done...

The next morning, Holywell reports Carteret's death to the authorities, glossing over the inconveniently supernatural details; Cotton backs up his claim simply to have found the body in the street. Holywell then informs the Doctor that there have been numerous mysterious disappearances of late; all of the victims have been young libertines, and Holywell believes that it is their voices he has heard in his seances. The Doctor, intrigued, asks Holywell to conduct another such seance that night so the Doctor can see for himself; in the meantime, Holywell takes the Doctor to a library of the arcane so he can research the history of the area for himself. Holywell has made a list of the men who have vanished, but has been unable to find a connection between them -- apart from the fact that they have all vanished within one square mile of Cheapside.

Turlough awakens in the company of Jeake and Flowers, who have been tending to him since their coach struck him down last night. He has recovered from his injures but can't remember exactly where Holywell's house was located, and thus has no way of getting back to the Doctor. Flowers sets off to the Diabola Club to investigate Poltrot's claim that Carteret had been playing cards with Sir Nikolas Valentine before his disappearance, but the nervous Jeake excuses himself to watch over the recovering Turlough, and they agree to meet that night at the theatre. Meanwhile, the two aliens discuss their client's quest; there have been no conclusive developments as of yet, and their client may be acting indiscreetly. That evening, Ned Cotton is accosted by the masked Lovemore, who claims to come as an angel of retribution -- and shoots the terrified Cotton through the chest before he can react.

At the Diabola Club, Flowers finds Poltrot playing cards with Valentine, who has promised to improve the former schoolmaster's present situation. The emboldened Poltrot asks Valentine why he never removes his gloves at table, but Valentine claims that this is no more than a gambler's superstition. Flowers interrupts their game to confront Valentine, demanding to know what so upset Carteret the night before, but Valentine professes his innocence. Flowers calms down, apologises for his rough manners, and introduces himself properly as a mathematician -- and the intrigued Valentine invites him to sit down and join the game. Later that night, when Turlough and Jeake arrive at the theatre to meet Flowers, Flowers seems strangely anxious and flees without speaking to them. The worried Jeake and Turlough give chase and corner Flowers in a deserted street, where Flowers begs them to help him, claiming that he is being pursued by devils which he cannot shake off. As Turlough and Jeake watch in disbelief, the street fills with the same clamour which Turlough heard the night before, and Flowers vanishes into thin air.

The power summoned by Holywell disperses, and as the Doctor slowly recovers from his experience, he realizes that he and Holywell had tapped into some sort of radio signal. Elsewhere, the disoriented Flowers materializes in the lair of Nikolas Valentine. This time, they shall play a new game...

The next morning, Holywell has fully recovered from his experience, but the Doctor is still unsure why his latent psychic ability has enabled him to detect radio signals. Hoping to find the source of the signals, he allows Hannah and Holywell into the TARDIS to watch him at work. Unfortunately, although he can still detect residual signals, the actual source is blocked, much to Hannah's disappointment. The Doctor asks Holywell to continue researching the history of Cheapside while he and Hannah seek out the local gossips and try to find a connection between the missing men. As they search for a reliable source, they see posters going up around Cheapside -- Major Billy Lovemore was seen riding away from the site of Ned Cotton's murder and is now wanted in connection with the crime. Holywell, meanwhile, discovers that similar spates of "vanishments" have been occurring in and around Cheapside for the past thirty years...

The terrified Flowers has been pinioned in a horrific room with walls like raw weeping meat, surrounded by the emaciated remains of those whom Valentine has already kidnapped, used and discarded. Flowers begs for mercy as Valentine connects him to the equipment in the room, but his captor seeks restoration and will do anything to achieve his goal. Flowers finds unfamiliar numbers and strange words flowing through his head, and as he struggles vainly to resist, Valentine urges him to give himself up to the power now flooding through him. As Flowers and the husks of the other men begin to chant sector co-ordinates and engine malfunction messages in unison, Valentine assures them that their task will soon be complete -- and then they can rest for all eternity.

Turlough and Jeake share breakfast, their appetites whetted by the odd events of the previous night; Jeake can hardly believe his own eyes, and agrees with Turlough that if they take their story to the authorities they will be considered mad. Jeake has learned of Carteret's death and the death of Ned Cotton in Cheapside, and he and Turlough visit the area and find the Doctor at a coffee house where Hannah has brought him to consult a local gossip. Introductions are made and stories are shared, and when the Doctor shows Jeake the list of missing men he identifies them all as members of the Diabola Club -- and recalls Flowers' intention to question a mysterious new member, Sir Nikolas Valentine. Hannah and Turlough fetch Holywell, while Jeake takes the Doctor to the club to investigate further. Since the Club is not a suitable environment for a young lady such as Hannah, she remains at home.

Jeake eventually spots Valentine, who is once again playing cards with Poltrot. Jeake and the Doctor interrupt, and Jeake sends Poltrot to fetch wine for his friends while the Doctor sits down to play a game with Valentine. Although initially irritated that they have driven Poltrot away, Valentine seems to become more interested when he learns that his new opponent is a Doctor. The Doctor is unable to learn anything more from Valentine, although he too notes Valentine's affectation of wearing gloves at the table. Valentine deals a final card and loses to the Doctor, but allows the Doctor to keep the card as a souvenir; it is the Ace of Hearts, a single red heart -- a valentine. The Doctor, still unsure what Valentine's real game is, sets off to wander the streets alone and think things over. Holywell returns home as well, but while hailing a cab Turlough and Jeake catch sight of Valentine leaving the club and decide to follow him to his home. The Doctor, meanwhile, hears the sound of the spirits again -- and this time, they're after him.

The phantom voices pursue the Doctor through the streets of London, but just as they are about to catch up to him Lovemore arrives on his steed and gives the Doctor a ride back to Holywell's. There, however, he drops the Doctor off and departs when it becomes clear that the card given to the Doctor by Valentine is in fact a homing beacon drawing the spirits to him. Holywell emerges to find the Doctor seeking some way to destroy the card; it will not tear, however, and as Hannah appears to have gone missing no fire has been set. Holywell has a box of matches on him, however, and the Doctor sets the card afire just as the spirits close in on him; this time, the psychic manifestations of Valentine's other victims have taken physical form, and Holywell can see their distress. The spirits disperse when the card is destroyed, robbing Valentine of his prey. Back in Valentine's lair, Flowers crows in triumph at his captor's loss, while Valentine becomes intrigued by this display of the Doctor's quick intelligence. Perhaps his mind could be the final component Valentine requires...

The Doctor determines that the circuitry within the card is designed to absorb the biodata of the first person to handle it, which explains why Valentine always wears gloves. Once the card has acquired a target it then acts as a beacon, summoning the collective spirits of the men Valentine has already kidnapped to transport its victim into his clutches. The Doctor uses a device of his own invention to erase the biodata print from the card he removed from Carteret's hand the previous night; it is now primed to acquire a new target, and the Doctor stores it in his Wisdon's Almanac for future use. Hannah arrives, claiming to have hidden when she heard the spirits approaching -- but the Doctor, his suspicions already aroused, points out that she is still wearing the same boots she wore when she rescued him under the guise of Major Billy Lovemore. Hannah, caught out, admits that she disguised herself as Lovemore to prove that a woman does not have to be a simpering simpleton confined to the kitchen. But the Doctor also points out that she showed an odd lack of surprise when told that the playing card was a homing beacon, and that she was using a voice synthesizer to disguise her voice while playing at Lovemore. Holywell listens in astonishment as Hannah admits that she is from another world, having hired a ship to take her in pursuit of the man who killed her parents -- the notorious psychopath Carthok of Daodalus. When his biodata print was detected on Earth, she took on the name of Hannah Fry in order to investigate discreetly, but was forced to take on the alternate guise of Billy Lovemore when it became clear that there were certain places on this primitive world where a woman by herself would attract unwanted attention. Now that this is explained, the Doctor suggests locating Valentine's home -- and suddenly realizes that Turlough is nowhere to be found...

Turlough and Jeake have followed Valentine to his house, which appears perfectly ordinary apart from a devilish glow in the attic; but when they break in they find the interior of the house a stinking, organic structure with walls like livid, raw meat. They attempt to confront Valentine in his attic, only to find that he is waiting for them -- and that the attic is defended by weapons which melt the gun in Jeake's hand where he stands. Valentine secures the helpless Jeake and Turlough to his equipment, intending to process them as he has his other victims -- emaciated husks who lie scattered about the room, most of them too weak to move. At that moment, the Doctor, Hannah and Holywell arrive, having extracted Valentine's home address from Poltrot. Holywell attempts to break in through the rear of the house while the Doctor and Hannah distract Valentine by calling him to the front door. As Valentine goes to greet his visitors, Jeake recognizes one of Valentine's emaciated victims as Flowers -- and Flowers, nearly too weak to talk, tells them that Valentine's game is nearly at an end...

Valentine welcomes the Doctor to his home, and shows no remorse when Hannah reveals that he murdered her parents. She forces him up to the attic at gunpoint -- but once there, the defense systems blast the gun out of her hand. This house is Valentine's spaceship, which was damaged in his haste to escape from his enemies; he has been trapped on Earth for the past thirty years, waiting for his biomechanical ship to repair the damage to itself. In order to do so it requires the stimulus of intelligent minds, and Valentine has been locating such individuals, draining them and discarding them when they are burnt out. The Doctor pleads with him to show reason, but he has grown to hate the Earth during his exile here and intends to rain down destruction upon his enemies once he departs. He requires only one more mind to complete his work, and although he had originally intended to use the Doctor, he now decides it would be more appropriate to use Hannah instead.