Kempson was born in Dartmouth, England, the daughter of Beatrice Hamilton (née Ashwell) and Eric William Edward Kempson, who was a headmaster. She was the wife of Sir Michael Redgrave; daughter-in-law of Roy Redgrave and Margaret Scudamore; mother of Vanessa, Lynn and Corin Redgrave; and grandmother of Natasha and Joely Richardson, Jemma Redgrave, and Carlo Nero.

In 1959 her husband was knighted, and she became, formally, Lady Redgrave. She never used this name professionally. In 2003, four days before what would have been her 93rd birthday, she died of a stroke at the home of her granddaughter, Natasha Richardson, in Millbrook, New York.

Kempson trained at RADA before joining the Royal Shakespeare Company. She married Michael Redgrave in 1935 and appeared with him many times on stage. She also appeared many times on film and television, most notably in the films The Captive Heart (1946); Tom Jones (1963); Out of Africa (1985), Uncle Vanya (1991); and the television series The Jewel in the Crown (1984).

Her 1986 autobiography, Life Among the Redgraves was published by Dutton. According to Publishers Weekly, "Lady Redgrave writes with candor, wit, restraint and some sadness about her background, beginnings in the theatre in 1932, marriage and motherhood, the trials of moving and the problems of being married to a handsome matinee idol."