Several of her early film roles were in mystery thrillers. She made her cinema debut in the Scotland Yard film "Gideon's Day" (1958) as Sally, daughter of Jack Hawkins's Detective Inspector. The director was her godfather John Ford. She played a potential murder victim in Michael Powell's cult thriller "Peeping Tom" (1960) and appeared in Otto Preminger's "Bunny Lake Is Missing" (1965). In 1972 she played the role of the barmaid Babs in Alfred Hitchcock's penultimate film "Frenzy". In the documentary on the film's DVD release, Massey mentioned that she originally auditioned for the much smaller role of the secretary Monica, a part for which Jean Marsh was cast. She also noted that her character's nude scenes in "Frenzy" were performed by body doubles. She appeared alongside her brother Daniel—they played siblings—in the horror film "The Vault of Horror" (1973).