Leighton's Broadway debut was as the Queen in Henry IV (1946) starring Laurence Olivier and Ralph Richardson during a visit to America of the Old Vic company, which performed a total of five plays from its repertoire before returning to London.
After appearing in two British films, including the starring role of Flora MacDonald opposite David Niven in Bonnie Prince Charlie (1948), the willowy blonde actress played the second female lead in Hitchcock's Hollywood film Under Capricorn (1949) starring Ingrid Bergman, Joseph Cotten, and Michael Wilding. She starred with Walter Pidgeon in the Metro-Goldwyn-Mayer crime/mystery Calling Bulldog Drummond (1951).
Leighton had three husbands: publisher Max Reinhardt (married 1947-divorced 1955); actor Laurence Harvey (married 1957-divorced 1961); and actor Michael Wilding (married 1964-her death 1976). She had no children.
She won the Tony Award for Best Actress in a Play for her performance in Separate Tables (1956); she won another Tony in that category for The Night of the Iguana (1962), playing Hannah Jelkes opposite Bette Davis as Maxine Faulk. Leighton was nominated for Best Actress in a Play for Much Ado About Nothing (1959) opposite John Gielgud and for Tchin-Tchin (1962) opposite Anthony Quinn.
She also had a noteworthy list of TV appearances, including Alfred Hitchcock Presents, Ben Casey and Burke's Law. She won the Emmy Award for Outstanding Performance by an Actress in a Supporting Role in Drama for Hamlet (1970). And she was nominated for an Emmy in 1966 for Outstanding Single Performance by an Actress in a Leading Role in a Drama for four episodes of Dr. Kildare.
For her film role as Mrs. Maudsley in The Go-Between (1970), Leighton won the British BAFTA Film Award for Best Supporting Actress. She received a BAFTA nomination for Best British Actress for her role as Valerie Carrington in Carrington V.C. (1955) and also received a Hollywood Academy Award nomination for Best Supporting Actress for The Go-Between.