Outside politics, Levy was a successful playwright who also wrote (and on occasion directed) for the movies. He was married for more than 40 years to the American-born screen and stage actress Constance Cummings; they had one daughter and one son. As an MP, Levy made an unsuccessful effort to abolish theatrical censorship in Britain, and towards the end of his life, he was the principal author of a report opposing the arguments for censorship made by Francis Aungier Pakenham, 7th Earl of Longford.
Levy's papers are held at the University of Sussex library.