Geeson's professional acting career started in July 1962, with an appearance in an episode of the television series "The Probation Officer". Her first major film appearances came in 1967, with roles in "To Sir, with Love" and "Berserk!". She followed these films with the comedy "Here We Go Round the Mulberry Bush" (1968). Geeson became well known as a result of a regular role in the BBC early-evening soap opera "The Newcomers". She also had a major role in the mid-1970s costume drama "Poldark" as Caroline Penvenen (later Caroline Enys).