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.

When HMS Scotia pays a visit to the French Riviera, the officers throw a lavish party to celebrate the engagement of Captain Robert Randall to Jill Eaton, a charming American girl; among the guests are Mary Carlton, Jill's American friend, and Antoinette, a vivacious redhead. However, when the last shore-boat is deemed unseaworthy, the girls are obliged to spend the night on ship. A series of hilarious complications ensue, as the officers attempt to keep the girls away from the beady eyes of Admiral Hewitt – who chooses this very night to board the Scotia.

Scotland Yard Inspector George Gideon starts his day off on the wrong foot when he gets a traffic-violation ticket from a young police officer. From there, his 'typical day" consists in learning that one of his most-trusted detectives has accepted bribes; hunts an escaped maniac who has murdered a girl; tracks a young girl suspected of involvement in a payroll robbery and then helps break up a bank robbery.

American scientist Dr. Frank Smith is brought to Britain to help the C.I.A. There is a defecting East block scientist they want him to debrief. The commies are less than amused and set Dr. Smith up for a murder.