Massey made her 1955 West End debut in The Reluctant Debutante when just 17. The play transferred to Broadway where she gained a Tony nomination for Best Supporting Actress, aged only 18, and met her first husband, actor Jeremy Brett.
The couple divorced in 1962 but together starred in a BBC screen adaptation of Daphne du Maurier's Rebecca in 1979, with Brett playing Max de Winter to Massey's Mrs Danvers.
Her West End credits include the 1962 production of Sheridan’s School for Scandal, directed by John Gielgud. The also appeared in Right Honourable Gentleman (1964), The Glass Menagerie (1965), The Prime of Miss Jean Brodie (1966) and Slag (1971).
Massey won the Best Actress BAFTA for her performance as Edith Hope in the 1986 BBC adaptation of Anita Brookner’s Booker Prize-winning novel Hotel du Lac.
Her recent television appearances included Tess Of The D'Urbervilles (2008), Oliver Twist (2007), and the BBC's version of Anthony Trollope's He Knew He Was Right (2004).
She played Baroness Thatcher in the 2006 television film Pinochet In Suburbia and was most recently seen in Poirot and Midsomer Murders in 2009.
Her other stage appearances included Moonlight at the Almeida and then the Comedy Theatre directed by David Leveaux in 1993 and the Royal Court's 1981 production of The Seagull directed by Max Stafford-Clark. In 1996 she played Elizabeth in Mary Stuart at the National Theatre directed by Howard Davies.
She won the 1983 Olivier Award for Best Supporting Actress for her role in The Importance of Being Earnest at the NT Lyttleton and on regional tour. She appeared in the production, directed by Peter Hall, alongside Nigel Havers, Martin Jarvis, Judi Dench and Zoe Wanamaker.
Massey was appointed CBE for services to drama in 2005. Her autobiography, Telling Some Tales, was published the following year. She is survived by her second husband, Russian scientist Uri Andres, and by the son of her first marriage, the novelist and illustrator David Huggins.