A salesman in Cuba takes up spying to support his spendthrift daughter.

In Havana, a very properly dressed British gentleman strolls into the vacuum cleaner store managed by James Wormold, and after being treated to a demonstration of the Atomic Pile vacuum cleaner and ascertaining that Wormold is a British citizen, cryptically states that he will being seeing Wormold again. On the street outside the shop, Havana police captain Segura, known as the "Red Vulture" for his affiliation with the Communists, questions Wormold's friend, Dr. Karl Hasselbacher, about the British vacuum cleaner customer. After Hasselbacher cautions Wormold about Segura's interest in his customer, the man follows Wormold into a bar and pulls him into the washroom, where he introduces himself as Hawthorne, a member of the British Secret Service. Hawthorne then offers Wormold ₤150 per month to become an agent and recruit a network of sub-agents to provide the London office with information about "the enemy." At his hotel room later that night, Hawthorne hands Wormold a copy of the Lambs' Tales and instructs him to use it to encode messages. In need of money to pay for the horse and concomitant membership in an expensive country club that his seventeen-year-old daughter Milly has requested for her birthday, Wormold accepts the assignment. Sometime later in London, Hawthorne unhappily reports to his superior, "C", that the only contact from "their man in Havana" has been a request to pay for an expensive membership in a country club. Upon receiving a curt message from London ordering him to recruit some agents, Wormold hurries to the country club, where he parrots Hawthorne's recruitment pitch to an engineer named Cifuentes and Prof. Sanchez, who regard him as a lunatic. When Wormold laments his miserable failure to Hasselbacher, the doctor advises him simply to "invent" the agents. Inspired, Wormold sends London a cable about his three new recruits, Cifuentes, Sanchez and a stripper named Teresa, who has "ties to important government ministers." One night, seeing a giant shadow of his vacuum cleaners, Wormwold is inspired by their weapon-like appearance and makes sketches of the Atomic Pile, informing London that a pilot he recruited named Montez, whose name he saw on an airline's roster of pilots, spotted them as he flew over a mountain range. Upon examining the drawings, Hawthorne notices that they look like giant vacuum cleaners and is about to voice his suspicion when C pronounces the weapons "more dangerous than the H bomb" and congratulates Hawthorne for his excellent judgment in hiring Wormold. Shortly afterward, Wormold and Hasselbacher are celebrating Milly's birthday at a nightclub when Segura stops by their table and flirts with Milly. Beatrice Severn, a British agent who has just arrived from London to help Wormold, eavesdrops on Segura's suggestive conversation and shoots him in the back with a bottle of seltzer water. After Segura leaves, Wormold, unaware that she is a British agent, introduces himself to Beatrice, who is equally unaware that he is the man to whom she is to report. Upon learning Wormold's name, Beatrice identifies herself and tells him that she has come to Havana with Rudy, who will work as their radio operator. The next day, Beatrice comes to Wormold's store and informs him that the Prime Minister wants photographs of the weapons and has asked to meet Montez. In reality, Montez is a name Wormold appropriated from the roster of a Cuban airline. Stalling for time, Wormold lies that Montez has lost his job piloting for the airline, but he will attempt to find him. Stopping at a bar, Wormold spots a comic strip in which a pilot crashes his plane and decides that Montez should experience the same fate. Upon returning to the office, Wormold states that Montez has agreed to fly a private plane into the mountains, an extremely dangerous task. Soon after, Beatrice and Wormold visit Hasselbacher at his home, and Beatrice becomes suspicious when she sees a copy of Lambs' Tales . When she begins to question Hasselbacher about his German ancestry, Wormold vouches for his friend. Their conversation is interrupted by a phone call, and after speaking with the caller, the doctor becomes ashen-faced and announces that Montez has died in a car crash. Worried that all of Wormold's agents may be in danger, Beatrice insists on warning them. Wormold takes her to the Ophelia Club where Teresa is performing, and when the police arrive, Beatrice and Wormold drape Teresa in a veil and haul her out a window onto the street, where they are apprehended by the police and taken to Segura for questioning. Segura explains that he has had Hasselbacher's phone tapped, then plays back a recorded phone call in which a man with a stutter informs the doctor of Montez's death. When Hasselbacher tells the caller that Montez was only to be frightened and not harmed, Wormold realizes that his friend is working for the enemy. Now questioning his friend's loyalty, Wormold goes to see him and finds him wearing a German officer's uniform from World War I. Hasselbacher, who blames himself for Montez's death, admits to decoding Wormold's cables and passing them to the enemy, who had threatened him with deportation unless he cooperated. Flabbergasted, Wormold sputters that he invented everything, to which the doctor responds that he "invented it too well." Soon after, Segura summons Wormold to his office where Cifuentes, whom Wormold had claimed never to have met, testifies that Wormold accosted him at the country club. Segura then demands that Wormold supply him with secret information and give him permission to marry Milly, or else he will be deported. Matters take a turn for the worse when Hawthorne informs Wormold that the department has learned an enemy agent plans to poison him when he gives the keynote speech at the upcoming European Trade Lunch. At the luncheon, Wormold assiduously avoids all food and drink. When his tablemate offers Wormold a slug of scotch from his flask and takes the first gulp, Wormold drops his guard. After draining the flask, Wormold is called upon to give his speech and Hubert Carter, seated across the table, offers him a shot of scotch for fortification. When Carter stammers, Wormold realizes he was the agent who called Hasselbacher. He drops his glass in fear, and after the scotch splashes onto a dog lying on the floor, the dog licks his fur and dies. Shortly afterward, Hasselbacher is murdered, and when Segura asks Wormold to identify the body, Wormold suggests that he investigate Carter. Unsettled by his friend's death, Wormold confesses to Beatrice that he is a fraud and sends her back to London. Later, Segura comes to the shop where Wormold, determined to secure the captain's gun to avenge Hasselbacher's killing, challenges him to a game of chess using miniature liquor bottles as chessmen. The bottles are to be drunk as they are captured, and because Segura is the superior player, he becomes inebriated, after which Wormold suggests that he would be more comfortable if he removed his gun belt. After Segura divulges where Carter lives and passes out, Wormold takes his gun and finds Carter. Wormold invites Carter to accompany him to the Ophelia Club, and before leaving, Carter instructs a colleague to meet them at the club. Outwitting Carter, Wormold takes him to a different club, and as they walk into the street, pulls out his gun. As Carter begs for his life, pleading that he is unarmed, Wormold fires but misses him. As Wormold walks away, Carter pulls out his gun and fires and Wormold shoots back, killing him. At the cemetery where the funerals of Hasselbacher and Carter are held on the same day, Segura presents Wormold his deportation papers and orders him to leave immediately for London. Arriving at the airport to see off Milly and Wormold, Segura hands Wormold the spent shells he fired at Carter. Upon reaching London, Wormold is escorted to Secret Service headquarters where Beatrice greets him and promises to wait for him. C, however, has realized that if the Admiralty ever learns about the folly, his agency will be dismantled. Consequently, he lies that he has learned the weapons have been dismantled and praises Wormold for his valor, adding that he has been recommended for a decoration. As Wormold joins Beatrice in the street, a vendor tries to sell him a toy weapon in the shape of a vacuum cleaner.