She was innate within Gorebridge, Midlothian, Scotland, to Presbyterian parents who disapproved of her becoming an actress. Still, she joined a Bristol Old Vic while still within her teens. Her large break come once she was selected to play Catherine of Aragon in the major BBC television series, The Six Wives of Henry VIII in 1971. Two or three years late, she processed the similar impact when a second Queen, Victoria, in the ITV period drama, Edward a Seventh (1975).

Crosbie's next major role wwhen as Margaret, long-enduring married woman of Victor Meldrew, in the British sitcom, One Foot in the Grave (1990). She likewise played Janet, a housekeeper to Dr. Finlay, in the 1993 revival of A.J. Cronin's popular stories. She played "Edith Sparshott" alongside Helen Baxendale in An Unsuitable Job for a Woman, and around 2003 played Jessie in the hit British film comedy Calendar Girls.

She is the mother of actor Selina Griffiths.