After a pierside mix-up with the Italian family of his fiancée, Able Seaman Knocker White (Sir Richard Attenborough) finds himself literally left holding the baby. Unable to return it before his ship sails, he enlists the help of his best friend Puncher Roberts (Sir John Mills) to smuggle the child aboard. But babies are surprisingly demanding, and gradually the whole crew is drawn into helping keep it fed and washed, and undiscovered. Even so, the officers above deck start to puzzle over the increasingly strange happenings on-board.