The daughter of Canadian actor Raymond Massey and British actress Adrienne Allen, Massey received a Tony Award nomination for her Broadway debut in 1957's The Reluctant Debutante.
She made her screen debut in 1958's Gideon's Day and appeared in such films as Peeping Tom, The Tall Guy, Frenzy, and Possesion. She played Miss Prism in a 2002 film version of The Importance of Being Earnest opposite Colin Firth and Rupert Everett.
Massey worked frequently on British television, including roles as Mrs. Danvers in Rebecca and Charlotte in The Cherry Orchard. She won a BAFTA Award for Screen Two.