She was born Wendy Margaret Hiller in Cheshire in England, daughter of Frank Watkin Hiller and Marie Stone. She made her professional debut as an actress in repertory at Manchester. She attracted the attention of George Bernard Shaw in the stage production of Love on the Dole, and he cast her in several of his plays, including Pygmalion, Saint Joan and Major Barbara.
She was nominated for an Oscar in 1938 for her first major film role in Pygmalion. She was nominated again in 1966 for A Man for All Seasons. She won the Best Supporting Actress Oscar in 1958 for the film Separate Tables.
She was made a Dame Commander of the Most Excellent Order of the British Empire in 1975 (see British honours system). For many years she was married to Ronald Gow, who adapted Walter Greenwood's novel Love on the Dole for the stage. Gow died in 1993.