Born in London, Sheen began her career training at the East 15 Acting School, and has appeared regularly on British television and in British films since 1988. On television she played Maureen Tacy in the series Doc Martin (2002), she had recurring roles as Nanny Simmons in Berkeley Square (1998),and as Nurse Ethel Carr in the series Bramwell (1995–98). She also appeared as four different characters in six episodes of The Bill between 1989 and 2004.

In 2007, she played the role of Lyn, opposite Ben Whishaw's Steven, in the world premiere of Philip Ridley's stage play, Leaves of Glass at the Soho Theatre, London. Also in 2007, she appeared in TV mini-series drama titled Fanny Hill, based on an erotic novel written by John Cleland. She played the role of Mrs Jones. She also played the mother of Jim Sturgess's character, Jamie, in Philip Ridley's 2009 feature film, Heartless. She appeared in the films Run Fatboy Run (2007) and Welcome to the Punch (2013), and was the titular Elizabeth in "The Trial of Elizabeth Gadge", a 2015 episode of Inside No. 9. In 2016 she played Elsie in the hit film adaptation of A Street Cat Named Bob.

She has also appeared in six Mike Leigh films: most recently in Mr. Turner (2014 film), in the female lead role of Shirley in High Hopes (1988); as Laughing Woman in Secrets & Lies (1996); as Maureen in All or Nothing (2002), as Lily in Vera Drake (2004) and as Gerri in Another Year (2010). Her role in High Hopes won her the Best Actress award at the 1989 European Film Awards.