The Doctor unexpectedly vanishes from the TARDIS, but returns just as Steven and Vicki are starting to become seriously concerned; however, he has no memory of where he has been, only vaguely recalling that he met “a dandy and a clown”. In his pocket, he finds an invitation card which, when placed on the console, causes the TARDIS to materialise on an island near Venice in the year 1609. Unsure why they have been brought here and suspecting that they are being led into a trap, the Doctor and his companions nevertheless cross the lagoon to the city; there, the Doctor is mistaken for Cardinal Bellarmine, a Catholic authority who is coming to Venice to pass judgement on Galileo Galilei’s invention, the “telescope”. The Doctor, Steven and Vicki are thus shown to guest quarters in the Doge’s palace, where the Doctor warns them to be very careful about their actions in this city. Venice has grown rich due to its prime location on a major trade route between Europe and the Orient, and the people of the city live in constant fear of Turkish spies mapping out the network of sandbanks which protects the city from invasion. Venice is ruled by shadowy committees elected almost at random to ensure that no one person acquires ultimate power, but there are still many noble families in the city whom it is unwise to annoy.

Galileo, who has no intention of revealing to the Doge that he stole the design of the telescope from Hans Lippershey in Germany, is testing his invention when he sees what appears to be a flying disc travelling from the Moon to the Earth. Disturbed by what he’s seen, he heads for a nearby tavern; shortly afterwards, an alien being emerges from the canal outside, encountering and killing Galileo’s landlord Carlo Zeno on the way. At the tavern, a stranger buys Galileo a drink after “accidentally” spilling his first, but Galileo is then accosted by a group of hot-headed youths who accuse him of disputing God’s pre-eminence in the heavens. Galileo tosses his drink in young Baldassarre Nicolotti’s face and prepares to take his leave, but his drink turns out to contain poison, and Nicolotti dies within seconds. Galileo flees the scene and encounters Steven, who has just stumbled across Zeno’s body. Both soon determine that the other is innocent of the murder, and since neither wishes to draw the authorities’ attention, they dispose of the body in the canal and go out drinking together.

That night, Vicki dreams of a flying creature named Albrellian who praises her beauty; the next morning, however, she finds scratches on her windowsill and realises that it was not a dream. Guards arrive to escort the Doctor to his next appointment, but Vicki becomes suspicious when she hears them discussing problems with Envoy Albrellian -- and she and the Doctor flee when the guards are revealed to be aliens wearing holographic disguises. The alien Jamarians retreat when real human guards arrive, and report their failure to their employer, Irving Braxiatel. Braxiatel, unable to understand why the Doctor would flee from his agents, concludes that the Jamarians tried to contact the wrong person. He sends them out to locate the real Doctor, and they eventually report that an old man is approaching Venice in a coach. To ensure that there are no misunderstandings, Braxiatel sends some of the other envoys from his conference to contact the old man -- the real Cardinal Bellarmine, who faints from joy upon seeing the aliens, believing that angels of the Lord have come to transport him to Heaven. Unaware of this, Braxiatel prepares to vacate his rented home in Venice and return to the island Laputa for the conference, but before leaving, he tells the Jamarians to take care of the impostor pretending to be the Doctor.

Steven wakes in Galileo’s home with a severe hangover, and Galileo lends him some clean clothing and tells him to invite his friends for dinner. On his way back to the Doge’s palace, Steven is accosted by the Nicolottis, who see his clothing, assume him to be Galileo and attempt to kill him. He is saved by a stranger named Giovanni Chigi, who realises that Steven is English and wants to know why so many Englishmen wearing odd fashions have recently arrived in Venice. Unable to help Chigi with his inquiries, Steven returns to the Doge’s palace to pass on Galileo’s invitation to his friends. They share a pleasant dinner until Galileo offers to demonstrate his telescope and finds that the lenses have been smashed. When he describes the odd sight which he witnessed the previous night, the Doctor and Steven realise that Galileo saw an alien spaceship approaching the Earth. Disturbed, they return to the Doge’s palace, where Albrellian is once again waiting on Vicki’s windowsill. Albrellian appears confused when the Doctor claims not to know what he’s doing here, and, apparently concluding that the Doctor is playing mind games with him in order to extract vital concessions, Albrellian kidnaps Vicki, telling the Doctor that he knows where she can be found once he’s ready to talk sensibly.

The Doctor fetches another telescope from the TARDIS, but he and Galileo are attacked by a Jamarian and Galileo damages the telescope tube beyond repair while fighting it off. However, he Doctor places the undamaged lenses from his telescope into the tube of Galileo’s, acquiring a working telescope which he and Galileo use to spot another flying saucer and triangulate its landing position. As they discuss their discovery and plan to rescue Vicki, they are attacked again, and this time when the Doctor overpowers the alien assassin he steals the holographic unit which it had been using to disguise itself as human.

Steven is forced to dive into a canal to avoid the vengeful Nicolottis, and while underwater he sees Braxiatel’s shuttle leaving an underground dock. He swims inside to investigate, only to find Chigi already there. Chigi and Steven retire to a tavern to compare notes, and Chigi explains that he followed the crowds of mysterious Englishmen to Braxiatel’s house and broke in to investigate further. As they talk, Chigi is surprised by the arrival of an old acquaintance -- William Shakespeare, who has been sent to Venice by spymaster Thomas Walsingham to investigate rumours of a conference being held by a mysterious new empire. Shakespeare is even more surprised to run into “Chigi”, and to recognise him as a man whom he’d thought long dead -- his old friend Christopher Marlowe.

Braxiatel is furious when Albrellian brings Vicki to Laputa, claiming that he’s in love with her. At first he thinks that Albrellian has kidnapped an innocent Venetian girl, but when Vicki explains that she’s a companion of the Doctor and tells him her story, Braxiatel realises that the situation is even worse. Laputa is the site of the Armageddon Convention, a conference which Braxiatel organised to limit the use of weapons of mass destruction in galactic wars. After much delicate negotiation, Braxiatel convinced most of the galaxy’s major powers to participate, but only if the Doctor -- who had become well-known for his campaign against the cruel Miniscopes -- acted as chairman. When Braxiatel’s people took the Doctor out of time to deal with the Omega crisis, they passed on Braxiatel’s invitation to him, but they carelessly gave it to an incarnation from an earlier timestream, and when they erased his memories of his own future he forgot what the invitation was for. Due to the confusion, Cardinal Bellarmine is now chairing the conference, and the delegates believe him to be the Doctor. Fortunately, Bellarmine apparently thinks that he is mediating between seraphim in a war in Heaven, and is using imagery from the Book of Revelations to settle disputes between the alien factions. Braxiatel thus decides to leave well enough alone. But this still doesn’t explain who is trying to kill Galileo, when Braxiatel had only ordered the Jamarians to sabotage his telescope in order to prevent him from spotting the delegates’ ships.

Marlowe explains to Steven and Shakespeare that he too is a spy for Walsingham, and that his apparent death in a pub brawl was faked in order to save him from Walsingham’s enemies; ever since, he has continued to act as a secret agent for England. Some years ago, while investigating charges of treason against Sir Walter Raleigh, he visited the American colony at Roanoke, where he saw flying demons kidnap the colonists. Somehow Marlowe survived and escaped, although some time later he was shot in a duel and the surgeon found and removed a strange piece of metal from his body. He has followed the trail of the missing colonists to Venice, and while trying to find out why they were congregating here he heard rumours of a mysterious conference; when he reported this to Walsingham, Shakespeare was sent to investigate further. Steven takes Shakespeare and Marlowe to the Doctor to tell their story, but as they ponder their next move a representative of the Doge arrives and instructs Galileo to present the telescope for inspection. The Doctor, however, needs Galileo’s help to find Laputa and rescue Vicki, and he thus orders Steven to use the stolen holographic unit to impersonate Galileo and present the telescope to the Doge, thus ensuring that history proceeds as it should. The Doctor, Galileo and Shakespeare rent a boat and strike out for Laputa, but they soon realise that another boat is on their tail -- with the Roanoke colonists, whose bodies are beginning to show signs of radiation sickness.

Braxiatel explains to Vicki that his people have surrounded the Earth with defensive satellites, and that the delegates’ flagships are all parked on the Moon to keep them out of harm’s way. But while dining in Laputa’s commissary, Vicki overhears part of a conversation between the Greld delegates, which makes it appear that Albrellian is trying to duck out of a vow they had all made to sacrifice themselves for a greater purpose. Before Vicki can warn Braxiatel, Albrellian kidnaps her again, this time explaining that he doesn’t really love her, but wants to take advantage of her knowledge of future history -- and that they must get away before it’s too late. The Greld are galactic arms merchants, who only agreed to participate in the Convention in order to sabotage it. While the Convention was being set up, the Greld attacked an isolated colony of humans, implanted hypno-controllers and fragments of a meta-cobalt bomb into their bodies, and scattered them across the planet to avoid detection. As soon as the Convention began, the Greld sent a signal summoning their victims to Laputa -- and since each human only contains a fragment of the bomb, the defenses on the island will not perceive them as weapons. Once they have all gathered together, the bomb will reach critical mass and explode, destroying the Convention.

Steven disguises himself as Galileo and presents the telescope to the Doge, who is quick to grasp the military applications of the telescope once he holds it the right way around. Before Steven can depart, however, he is caught and challenged to a duel by Tomas Nicolotti, father of Baldassare. To save Galileo from being hunted down and killed, Steven must agree to the fight though he knows he can’t win. Marlowe offers to take his place using the holographic disguise unit, but he loses the duel and is fatally wounded. The desperate Steven takes Marlowe to Braxiatel’s home and uses the skiff in the docking port to take him to Laputa for treatment, but despite his best efforts, Marlowe dies on the way. While tending to the wound, however, Steven finds a metal device buried within Marlowe’s body. Meanwhile, the Doctor, Galileo and Shakespeare reach Laputa moments ahead of the colonists, who are showing ever more advanced signs of radiation sickness as the fragments of the bomb come into close proximity. The Doctor has guessed the significance of their symptoms, but although he manages to warn Braxiatel of the danger the colonists all assemble on the beach before Braxiatel can launch his floating island into the air. However, the bomb does not explode, indicating that a vital component is still missing.

Albrellian takes Vicki to the Moon, intending to depart with his prize -- only to find the Jamarians looting the delegates’ ships. Braxiatel had chosen them as his servants since they were an isolated race with no special loyalty to any of the races attending the Convention, but he has underestimated their ambition; they intend to take advantage of their position to loot the other races’ ships and use the stolen technology to create an empire of their own. Realising how badly he and Braxiatel have miscalculated, Albrellian steals the telepathic data storage unit which the Jamarians were using to teach them how to use their stolen technology. He and Vicki escape and return to Laputa to warn Braxiatel of the danger, but as the Jamarians turn on Braxiatel, Shakespeare grabs the storage unit, empties its contents into his mind, and rushes off to steal a skiff and return to King James, bearing knowledge of new technology which will enable England to conquer the world.

The Doctor and Vicki pursue Shakespeare in another skiff, and Braxiatel grounds the others to prevent the Jamarians from following while he pilots the flying island towards England in pursuit. At that moment Steven’s skiff arrives, bearing Marlowe -- and the fuse of the meta-cobalt bomb. Marlowe’s hypno-controller had been removed by the surgeon who operated upon him after his duel, preventing him from receiving the orders to travel to Laputa with the other colonists; however, if Steven lands, the proximity of the fuse will detonate the rest of the meta-cobalt bomb. Accepting responsibility for his actions, Albrellian flies up to the approaching skiff under his own power, removes the detonator from Marlowe’s body and flies away with it. Following Albrellian’s instructions, Steven jams the skiff’s hatch open and leaps out as it lands, and the Jamarians pile in, intending to use this one functioning skiff to pursue Shakespeare and recover the data storage unit. Before they can launch it, however, Albrellian uses the hypno-controller to send the Roanoke colonists into the skiff. The Jamarians launch too late, and Albrellian waits for the skiff to clear Laputa before flying towards it with the detonator, causing the bomb to reach critical mass and explode.

Using the knowledge he’s acquired from the data storage unit, Shakespeare pilots his skiff to Hampton Court Palace, where his theatrical troupe is performing Macbeth for King James. Unable to interrupt the King’s entertainment, Shakespeare must take part in the performance himself when he learns that the actor who was to play Lady Macbeth has fallen ill. The Doctor and Vicki thus catch up to him, and take on the roles of a doctor and his servant in order to get close to Shakespeare on stage. The explosion of the Jamarian shuttle distracts the members of the court, giving the Doctor the opportunity he needs to force-feed an amnesia pill to Shakespeare and erase his memory of the past 24 hours. The Doctor and Vicki then return to Laputa, where they learn that the Convention has come to a successful conclusion, with the delegates all unaware of what has transpired outside the convention hall. Braxiatel gives amnesia pills to both Galileo and Cardinal Bellarmine and returns them to Venice to resume their ordinary lives, and the Doctor and his companions depart while Braxiatel vows to give up politics and take up collecting instead.