A swimming pool cleaner and a suicidal housewife set out on the run and are pursued by her corrupt lobbyist husband.

The film follows Jack Hopkins (played by Michael Craig), an aircraft designer with a passion for traction engines. His boss (played by Cecil Parker) is eager to sell a new supersonic jet plane that Jack has designed to American millionaire Paul Fisher (Alan Hale, Jr.). The first encounter between Fisher and Jack goes badly, and tensions only heighten after Fisher's daughter Kathy (Anne Helm) damages Jack's prize traction engine "The Iron Maiden", rendering it impossible to drive solo. Jack is desperate to enter the annual Woburn Abbey steam rally with the machine, but his fireman is injured and unable to participate. When all seems lost the millionaire himself is won over by Jack's plight and joins him in driving the engine; the two soon become firm friends.

Penniless Lord Whitebait's plan to save his sinking fortunes is to open stately Whitebait Manor to the public. But the public ignores his gesture, and his fortunes fade even further, with a stream of debts threatening to run into a deluge when his daughter's fiancé demands a plush and costly wedding. Where is the cash to come from? Whitebait and his servant Spankforth's answer is a scam involving the theft of a valuable painting from the Manor. How could such a cunningly original ruse fail?

An American art student in England falls in love with a beautiful Englishwoman. It turns out that she's a nudist, and in spite of his misgivings, he decides to join her at her nudist camp.