She began her career primarily working on British television series, with a leading role on The Newcomers from 1965 to 1967, before making her major film debut in To Sir, with Love (1967).

[2][4] Geeson's professional acting career started in July 1962, with an appearance in an episode of the television series The Probation Officer.

Geeson's other films include Prudence and the Pill (1968), Three into Two Won't Go (1969), 10 Rillington Place (1970), Doomwatch (1972), Brannigan (1975), starring John Wayne, and The Eagle Has Landed (1976).

In addition to her film and television work during this time, Geeson also performed in theatrical productions for the Royal Shakespeare Company as Lavinia in Titus Andronicus and as Viven 532 in Section Nine (both 1973).

She also had roles in stage productions of Next Time I'll Sing to You (1980) and The Real Thing (1985), both in London, before making her Off-Broadway debut in The Common Pursuit in 1987.

Geeson relocated from London to Los Angeles in 1984; there she began appearing in American television, including a role as a series regular in the sitcom Mad About You, playing the hostile neighbour, Maggie Conway, from 1992 to 1999.