Already an experienced stage actress, she did not make her speaking debut in film until the age of twenty-four in The Queen of Spades (1949), although she had played an uncredited minor role in Love on the Dole eight years earlier. She went on to appear in several prominent film roles over the following three decades, winning a British Film Award for The Divided Heart (1954) and the Berlin Film Festival Award for Woman in a Dressing Gown (1957). She also appeared in the role of Mildred in the controversial 1959 film Sapphire.

On television, Mitchell was voted Television Actress of the Year for 1953 by the Daily Mail newspaper, mainly for her role as Cathy in the Nigel Kneale / Rudolph Cartier adaptation of Emily Brontë's novel Wuthering Heights. The following year, she appeared in another Kneale / Cartier literary adaptation when she took the role of Julia opposite Peter Cushing as Winston Smith in their controversial and well-remembered adaptation of Nineteen Eighty-Four, which was to prove her most memorable role on the small screen. She continued to act occasionally on television until the late 1970s, appearing in guest roles in series such as Out of the Unknown (in 1966); her final screen role was in the BBC science-fiction series 1990 in 1977.

Outside of acting, Mitchell was also an established writer, penning several books for children and adults as well as winning awards for playwriting. She wrote an acclaimed biography of the French writer Colette, and her own autobiography was published in 1957.

Mitchell was married to the film and theatre critic David Monsey, and died of cancer in 1979, at the age of fifty-three.