London-based gangster George Thomason and his right-hand man, Ken Pile, an animal lover with a stutter, plan a jewel heist. They bring in two Americans: con artist Wanda Gershwitz and weapons expert Otto West, a stupid and mean-spirited anglophobe. Wanda and Otto are lovers, but they hide this from George and Ken, pretending to be siblings, so Wanda can work her charms on them. The heist is successful and the gang escapes with a large sum in diamonds. They hide the diamonds in a safe in an old warehouse; soon afterward, Wanda and Otto betray George to the police and he is arrested. They return to collect the diamonds, with Wanda planning to double-cross Otto as well, but find that George has moved them. In Ken’s fish tank, Wanda discovers the key to the safe deposit box containing the diamonds and hides it in her pendant.
Wanda decides to seduce George’s barrister, Archie Leach, so he can persuade George to plead guilty and give up the location of the diamonds. Archie is in a loveless marriage and quickly falls for Wanda. Otto is jealous, and his interference causes Wanda and Archie’s liaisons to go disastrously wrong. Wanda accidentally leaves her pendant at Archie’s house, which Archie’s wife, Wendy, mistakes for a gift for her. At Wanda’s insistence, Archie recovers the pendant by staging a burglary. Eventually, Archie, feeling guilty, ends the affair.
George asks Ken to kill the Crown’s only eyewitness to the robbery, an unpleasant old woman who owns three small dogs. Ken tries three times, but each time accidentally kills one of her dogs instead. This causes him great distress, but the last dog’s death gives her a fatal heart attack, so he is successful. With no witness, George seems poised to be released. He gives instructions to Ken, revealing the location of the diamonds, but Otto learns Ken now knows their whereabouts. Otto tries to force Ken to reveal the place by eating Ken’s pet fish, leaving Ken’s favourite, named Wanda, until last. Ken reveals that the diamonds are at a hotel near Heathrow Airport.
With Otto’s knowledge and Wanda’s key, the pair wants George to remain in jail. At his trial, defence witness Wanda unexpectedly gives evidence against him. When Archie, stunned, flubs his questioning and inadvertently calls her “darling”, Wendy realizes that Archie has had an affair and declares their marriage over.
With no career and no marriage, Archie resolves to cut his losses, steal the loot himself and flee to South America. Promised less jail time, George tells Archie that Ken knows where the diamonds are. Archie sees Wanda fleeing the courthouse, pulls her into his car and races to Ken’s flat. As Archie runs into the building, Otto steals Archie’s car, taking Wanda with him. Ken and Archie give chase. Otto and Wanda recover the diamonds, but Wanda double-crosses him and leaves him unconscious in a broom cupboard before leaving to catch a flight out of the country. Otto recovers, shoots his way out, and makes his way to the airport tarmac, where he is confronted by Archie. Otto is about to kill Archie, but Archie stalls him by taunting Otto about American failures such as the Vietnam War. Ken arrives, driving a steamroller, seeking vengeance for his fish. Otto, who has stepped in wet concrete and cannot move, is run over but survives. Archie and Wanda board the plane and Otto, clinging to the window outside, curses them until he is blown off during takeoff.