After being jilted by his fiancee, Arthur Pilbeam (Arthur Askey) wants a job where he will encounter no women. He is sent to a lighthouse on a remote Scottish island which is being run as a meteoroligical station where he is supposed to be the only inhabitant. However, Jane (Vera Frances), a young girl, has stowed-away on his boat. She is looking for her uncle on the neighboring island. Then model Bobbie turns up - her boat has been torpedoed. With the arrival of another boatload of survivors, bringing the total occupancy of the island to 13, things are getting a little crowded. That's when they all start to disappear, one by one...