Greenwood's most notable screen appearances were as Gwendolen in The Importance of Being Earnest (1952) and opposite Dennis Price in the black comedy, Kind Hearts and Coronets (1949). She also had a long stage career, appearing with Donald Wolfit's theatre company in the years following World War II. She died (of a heart attack) in London, England. Her last film was Little Dorrit, made in the year of her death.