A musical and comedic bit of fluff without any other pretensions, The Lady Is a Square plays off the popularity of Frankie Vaughan to help carry the story as Johnny Burns, a young man with a passion for pop music. He insinuates his way into the home of the widowed Frances Baring (Anna Neagle) by pretending to be a piano tuner, in reality, he has fallen for her daughter Joanna (Janette Scott). He soon learns that the widow, dedicated to promoting a series of classical music concerts, has no cash. More than willing to help out, he takes on the job of butler and then sets his sights on getting his own hit recording out. In spite of the widow's aversion to pop music, and her aversion to his interest in her daughter, Johnny keeps at his goal of stardom. Notable in this stock storyline is the character of Johnny's brash manager, played by up-and-coming Anthony Newley, about to make it big with Stop the World - I Want to Get Off.