A Danish freighter, the SS Helvig, is stopped en route from New York to Copenhagen by British contraband controls. The officials tell Captain Hans Andersen he will be able to leave the British port the next day. They invite him ashore for dinner that evening and issue shore passes for him and his First Officer.

Later that evening Andersen finds that the passes have been taken from his cabin. After a search of the ship it is determined that two passengers are missing. One is Mrs Sorensen, a spirited English woman who the stern but charming Andersen had earlier chastised for her refusal to wear a lifejacket. The other is a talent scout named Mr Pigeon. There is no apparent connection between Pigeon and Mrs Sorensen, and the only clue as to their whereabouts is a newspaper cutting that suggests they are going to catch a train to London.

The angry Andersen rows ashore, determined to find his errant passengers. At the station, Mrs Sorenson attempts to call her aunt in London but instead speaks to a female secretary called Lang. She and Mr Pigeon board the train, with Captain Andersen in close pursuit. When they alight in London, Andersen confronts Mrs Sorensen. She initially tries to lose him but then assures him she will get back to the ship before morning.

The pair head out into London, a city plunged into darkness and confusion by the blackout. After some banter, Andersen invites Mrs Sorensen to dinner. They take a taxi to The Three Vikings, a Danish restaurant owned by the brother of the Helvig's First Officer.

The couple enjoy a hearty meal and become more attracted to each other as the evening wears on. After leaving the restaurant they go to visit Mrs Sorensen's Aunt Kate. As they search the house it becomes apparent that Aunt Kate is not there. Instead, Lang the 'secretary' and two dour men with guns are waiting for them. They ask the whereabouts of Mr Pigeon, which are revealed after he impatiently telephones the house looking for Mrs Sorensen.

Mrs Sorensen and Andersen are bundled into a car and driven away. When they get to their destination, Andersen refuses to get out of the car and is knocked unconscious. When he comes to, Mrs Sorensen is being questioned by Von Dyme, a German agent. It is revealed that she and Mr Pigeon are British spies and have encountered Von Dyme before. He believes she has come to London to deliver some coded information to the Admiralty. After Mrs Sorensen asks for one of her cigarettes Von Dyme realises the information is written inside it. The message contains the neutral names under which German vessels sail the Atlantic. Von Dyme plans to give false information to the British that will implicate an American ship as a disguised German one. He hopes that stubbornness on both sides will provoke a war between Britain and America.

The Captain and Mrs Sorensen are tied up and left together in the basement. Andersen escapes and goes to get help. He switches on the lights in the building and escapes during the ensuing disturbance when officious blackout wardens come to investigate. Returning to the Three Vikings, he enlists the help of the Danish staff to rescue Mrs Sorensen and catch the spies.

While the Danes help Andersen retrace his steps, Lang and Von Dyme rendezvous with a British agent and pass on the false information. Andersen finds his way back to the basement where Sorensen and Pigeon are being held and the three of them escape. Von Dyme catches up with Andersen and, after a shoot-out, Andersen knocks out the spy with a plaster bust and leaves him for the police.

Andersen, Pigeon and Sorensen make it back to the ship by morning and the Helvig sets off for Copenhagen. Mrs Sorensen enters the dining room, once again without her lifejacket. She is called into the Captain's cabin, where she tells Andersen that the British officials were not fooled by his absence from dinner the previous evening. Instead of bickering as before, the couple embrace passionately.