Massey was born in London in 1933. He was educated at Eton College and King’s College, Cambridge. He was a member of the noted Massey family, which included his father, Raymond Massey, his sister, Anna Massey and his uncle Vincent Massey, the first Canadian-born Governor General of Canada. His mother was the actress Adrianne Allen. Living with his mother after his parents’ divorce, Massey rarely saw his father through most of his adult life; however, they were cast as father and son in The Queen’s Guards (1961). Massey made his film debut as a child in Noël Coward’s flag-waver, In Which We Serve (1942) – Coward being his godfather. He would later play Noël Coward in the 1968 Julie Andrews vehicle, Star!, a performance for which he won a Golden Globe Award and received his sole Academy Award nomination. He first made a major impression as an adult as Laurence Olivier’s son-in-law in the stage and screen versions of John Osborne’s The Entertainer. Massey appeared in numerous British films from the 1950s onwards, including Cromwell, The Cat and the Canary, The Jokers, The Vault of Horror, Mary, Queen of Scots, Victory!, and In the Name of the Father.

Other highlights of his career were his stage roles, especially that of the German conductor Wilhelm Furtwängler in Ronald Harwood’s Taking Sides; Massey won the 1995 Olivier Award for his performance. He recreated the role for Broadway a year later earning a Tony nomination. His other stage appearances included musicals such as She Loves Me, Gigi (as Gaston), and Stephen Sondheim’s Follies (as Benjamin Stone), for which he won another Olivier Award. In the 1980s and 1990s, he also appeared with the Royal Shakespeare Company in productions such as Love’s Labours Lost, Measure for Measure and The Time of Your Life, the latter alongside John Thaw. On television, highlights include The Crucible (1980) as Reverend Hale, The Golden Bowl (1972) as the Prince, in the Inspector Morse episode “Deceived by Flight” as Anthony Dunn, again with John Thaw, and his performance as an AIDS patient in Intimate Contact (1987). With Jeremy Brett as Sherlock Holmes, he played a U.S.Senator in “The Problem of Thor Bridge” season 5, Granada Television, 1990. He died in London after a three-year battle with Hodgkin’s lymphoma, and was buried at Putney Vale Cemetery. Massey worked in theatre throughout his cancer treatments, rarely missing a performance.