Geeson's father was an editor for the National Coal Board magazine while her mother worked in the box office at the London Coliseum cinema.

[2] Geeson studied at Corona Stage Academy from 1957 to 1966, during which time she played small non-speaking roles in several movies, including Expresso Bongo (1959), The Millionairess (1960), Spare the Rod (1961), The Young Ones and Carry On Regardless (1961).

She played a schoolgirl in The Great St Trinian's Train Robbery (1966), and appeared as a girl guide in Don't Raise the Bridge, Lower the River (1968).

In December 2014 until January 2015, Geeson played the Good Fairy at Theatre Royal Windsor in their panto Beauty And The Beast.

[3] Geeson married television personality William G. Stewart in 1976 and the pair had two children together.