Born in Willesden, London, Barker is the daughter of Ronnie Barker and Joy Tubb. As an actress she worked mostly in theatre. Her television debut came in the film Frankie and Johnnie (1985). The same year she appeared in episodes of the television sitcoms Open All Hours (with her father) and Fresh Fields, then in 1987 she was in the film Wish You Were Here and also in Agatha Christie's Miss Marple: At Bertram's Hotel. Other parts came in The Widowmaker (1990) and the crime series Maigret (1992) with Michael Gambon. In 1998 she appeared in the play Mum, which was written by her father.
Her younger brother, Adam, was also an actor and is still seen on television as DC Potter in repeats of Wycliffe. Her elder brother, Larry, retired after a successful career in advertising.