Jane and Timothy Dawes meet in a park, soon after their graduation, to plan their lives. They agree to get married, and do so in secret, but Timothy's parents have urged him to ask his various influential uncles—a Minister, a Foreign Office official, a General, a scientist—to find him suitable employment. He and Jane, however, decide that he must take the first job that he is offered. A passing tramp offers them £7 a week to look after his mobile piano for a month, and, upon accepting, they discover that when the piano plays it gives everyone within earshot an irresistible desire to dance!
After attempts by the Minister of Pleasure and Pastime (Timothy's Ministerial uncle) to ban the disruptive music, the piano vanishes, and Timothy enlists his scientific Uncle Zed to take them in his flying saucer to retrieve it. When it is found, the tramp reappears to tell them that their month is up and the piano must be passed on to another couple. He also reveals that he is a hitherto unknown uncle of Timothy (whose parents had referred to "the one we don't mention"). Timothy and Jane look forward to the future with confidence.