Edney first notable role was as Heather MacLeod in the 1986 film Highlander. She returned to the role again in the 2000 film Highlander: Endgame.
In 1987 Edney performed the title role in the TV production of The Dark Angel with Peter O'Toole. In 1990, she appeared in the Bruce Beresford directed film Mister Johnson alongside Pierce Brosnan and Edward Woodward.
Her many television appearances include a leading role in the TV series Lost Empires, based on the novel by J.B. Priestley, with Colin Firth in 1986. She has also appeared in episodes of Rosemary & Thyme, Inspector Morse, Lewis and Wallander.
In 1994, she played the role of Louisa Gradgrind in the television adaptation of Charles Dickens' novel Hard Times. In 2012 she played Queen Charlotte in The Madness of King George III, in a revival at the Apollo Theatre.