Dr. Tony Burke (Leslie Phillips) is in love with Ophelia O’Brien (Angela Scoular), but doesn’t have time to propose to her as she leaves for a cruise to the Mediterranean. Also, on-board the cruise ship is an old school chum of Burke’s who plays “Dr. Dare” on a very popular television series, and to whom women flock. Burke decides to join the cruise, but is first apprehended as a stowaway, and then becomes the Captain’s steward. For Burke, trying to talk to Ophelia is a hard enough task, but he meets some funny characters on-board, such as a pools winner, and a very stubborn Captain.