London-based gangster George Thomason finds himself embroiled in a complex jewel heist with his loyal right-hand man, Ken Pile, who happens to be an animal lover with a pronounced stutter. To pull off this ambitious plan, they enlist the help of two Americans: the witty con artist Wanda Gershwitz and the aggressive weapons expert Otto West, an anglophobe with a short fuse. Although Wanda and Otto pretend to be siblings, their romantic involvement is clear, and Wanda uses her charm to manipulate both Ken and George to serve their own interests.
The heist goes off without a hitch, and the gang escapes with a hefty sum in diamonds, which they decide to hide away for safekeeping. However, the plot thickens when Wanda and Otto decide to betray George, leading to his arrest. As they return to claim the diamonds, Wanda plans to double-cross Otto as well, but their scheme hits a snag when they discover that George has moved the loot to a safe deposit box, entrusting the key to Ken. In a rather clever twist, Wanda spies Ken stashing the diamonds in his fish tank, and seizes the opportunity to steal the gems, hiding them within her locket.
To learn the location of the safe deposit box, Wanda sets her sights on seducing George's barrister, Archie Leach. Despite being trapped in a loveless marriage, Archie quickly becomes smitten with Wanda. However, their clandestine encounters are complicated by Otto's jealousy. In a series of comedic mishaps, Wanda inadvertently leaves her locket at Archie's home, where his wife Wendy finds it and assumes it is a gift. This leads to a comedic chase as Archie attempts to recover the locket, all while navigating the interferences caused by Otto.
As tensions rise, George instructs Ken to eliminate the elderly eyewitness to the robbery, Eileen Coady. Although Ken's attempts at this grim task go awry, culminating in the accidental deaths of her small dogs, his last blunder inadvertently causes Mrs. Coady to have a heart attack, thereby removing her as a witness. With no one to testify against him, George seems set for release; however, Otto has different plans. In a desperate attempt to extract the diamond's location from Ken, Otto resorts to unorthodox torture methods.
Even with all the machinations in play, Wanda and Otto's success hinges on ensuring George stays behind bars. During George’s trial, Wanda unexpectedly twists the knife by providing testimony that implicates him further. Archie, taken aback by her betrayal, fumbles his questioning, leading to disastrous results. Realizing everything is falling apart, he decides to join forces with Wanda. Their plans intersect as they race to Ken's flat for the diamonds, navigating through a comedy of errors that ensues when Otto and Wanda retrieve the stash but tragically fall into each other’s traps.
The climax of this chaotic affair brings them to Heathrow Airport, where Otto’s pursuit of revenge and the diamonds leads to a showdown on the tarmac. Meanwhile, Ken, seeking justice for his beloved fish, appears on a steamroller, culminating in a hilarious finish where he runs over Otto, leaving him stuck in wet concrete. The zany escapades conclude with Archie astonishingly joining Wanda aboard her flight to Rio, while Otto’s efforts go to comedic waste.
In a charming epilogue, we learn that Archie and Wanda found happiness together in Rio, raising a large family, while Ken embraced a unique role at SeaWorld, and Otto improbably became the Minister of Justice for South Africa.
