Havana in the 1950s, before the Cuban revolution. Jim Wormold, a vacuum cleaner salesman abandoned by his wife, is under financial pressure from the expensive demands of his teenage daughter Milly. At his shop he is bemused by a visit from a well-dressed Englishman, whose movements are being watched by the police chief Captain Segura (nasty enough to have earned the nickname 'The Red Vulture').

In the comparative privacy of the toilet at Sloppy Joe's bar, the Englishman identifies himself as Hawthorne, in charge of the British Secret Service's Caribbean network. Offering a tempting salary with expenses, he invites Wormold to become "our man in Havana"; at a later meeting he explains the tools of the trade, including secret ink and a copy of Lamb's Tales from Shakespeare, the code source for transmitted messages. Urged to recruit his own agents, Wormold awkwardly canvases the prospects at Havana's country club, where Segura has arranged stabling for Milly's horse. When Wormold fails to enlist anyone, his sad-eyed German friend Dr Hasselbacher offers the solution: concoct imaginary information, and imaginary agents.

Wormold sends London his first report, with details of his supposed assistants: air pilot Montez, engineer Cifuentes, Professor Sanchez (all culled from the club register), plus Teresa, a dancer at the Shanghai Theatre. Using his vacuum cleaners as a model, he also sends drawings supposedly representing new weapons of war, under secret construction in the mountains. At least they convince Whitehall.

Serious ramifications follow. Dr Hasselbacher's flat is ransacked in an effort to pressure him to work for 'the other side'. Meanwhile, Whitehall sends Wormold reinforcements: a secretary and a radio operator. Beatrice Severn, the comely secretary, insists London needs photographs of the installation, to be taken by Montez. Inspired by a comic-strip, Wormold decides to wriggle out of his predicament by announcing the agent's death during the mission. Reality takes over when a phone call alerts the shaken Dr Hasselbacher to the death of a patient, Montez himself, in a car crash. Shortly afterwards another club member, Cifuentes, is dumped bound and gagged outside Wormold's shop.

Harassed by thugs, Hasselbacher, it turns out, has been decoding Wormold's telegrams in the belief that their information was false; Montez's death now convinces him otherwise. At Hawthorne's base in Kingston, Jamaica, Wormold learns that he himself is a murder target: there are plans to poison him at a business lunch. On the flight back he meets Humphrey Carter, a fellow salesman en route to a lunch meeting of European traders, where Wormold is due to make a speech. The lonelyheart Beatrice, in love with Wormold, pleads with him not to go; but through good luck and avoiding food he steers clear of poisoning - unlike another lunch guest, a dachshund. He also learns his assassin's identity from Carter's stammer, previously heard in a tapped phone conversation.

Bowing to pressure, Wormold agrees to share any information he gathers with Segura, who increases his grip by requesting Milly's hand in marriage and forcing him to identify Dr Hasselbacher's body, found in the street. Wormold finally tells Beatrice of his frauds and advises her to leave; she refuses. Equipping himself with Segura's gun after Segura passes out during an alcoholic game of checkers, Wormold tracks down Carter to a bar. Out on the street, the two exchange gunfire. Two funerals follow: Hasselbacher's and Carter's. Segura presents Wormold with deportation papers; he explains he doesn't feel safe with him around. At the airport, Segura slips the incriminating bullets that killed Carter into Wormold's hand and promises to look after Milly's horse.

Back In London, Wormold faces his spymasters, who have just been informed by a blithely apologetic Hawthorne that the Havana reports were pure fiction. Sensing that sweeping under the carpet is needed, the Service head, 'C', retires Wormold from active duty, promises him an OBE, and orders his drawings destroyed. Outside, Milly eyes a luxury car parked on the street, while Wormold and Beatrice, happy together, notice a street seller offering toy weapons shaped like vacuum cleaners, clearly marked 'Made in Japan'.