[5] She attended Dunfermline High School, and growing up was a big fan of George Bernard Shaw, who influenced her later writing.
[5] Television audiences first became acquainted with her as the sole female in the late 1960s comedy show Do Not Adjust Your Set, which also featured David Jason and three future Monty Python members; Terry Jones, Michael Palin, and Eric Idle.
[5] In the 1970s, she was a member of director Frank Dunlop's repertory company in London's Young Vic Theatre, appearing in several productions including Scapino (1974) and beginning her career as a playwright with some children's shows.
[5] Coffey had a few supporting film roles: Sidonia in Waltz of the Toreadors (1962), Peg in Georgy Girl (1966), Soberness in Far from the Madding Crowd (1967), and Mrs E. in Vivian Stanshall's Sir Henry at Rawlinson End (1980).
Apart from Do Not Adjust Your Set, her television appearances included the Stanley Baxter series (1968, 1971), Girls About Town (1970–71), Hold the Front Page (1974; which she also created), End of Part One (1979) and The Adventure Game (1980).