Born in London, she was a niece of Nancy Astor, and made her stage debut in the Little Revue (1939. During the 1950s she made her name as a sidekick to such comedy greats as Alastair Sim and Margaret Rutherford in films such as The Happiest Days of Your Life (1950) and the St Trinian's series.
Grenfell is now best remembered for her one-woman shows and monologues, in which she invented roles including a harassed nursery teacher (George, don't do that). She gained additional popularity as a result of her frequent appearances on the BBC's classical music quiz show, Face the Music