In 2001, she had roles in Enigma, and Tempted with Burt Reynolds, Peter Facinelli and Michael Arata. In 2004 she played the part of Andromache in the big-budget movie Troy. In Jan 2005 she created the role of Janey in the world premiere of Earthly Paradise at the Almeida Theatre and on 30 October, 2005 she appeared on stage at the Old Vic theatre in London in a 24-hour play, Night Sky, alongside Christopher Eccleston, Bruno Langley, David Warner, Navin Chowdhry and David Baddiel.
As of 2007 Burrows plays attorney Lorraine Weller on ABC's Boston Legal (Season 4).
In 2008, she appeared in the independent film, The Guitar, which made its debut at the Sundance Film Festival, as well as in a starring role in the heist film The Bank Job.
In a 1999 interview with Film Unlimited, Burrows revealed that she is bisexual. For a number of years, she was involved with film director Mike Figgis, and she starred in some of his films, including Miss Julie - one of the first films to experiment with multi-camera views, and Figgis' quad-screen film, Timecode.
Since the ending of that relationship, she has been romantically linked with actress Fiona Shaw. Neither actress has publicly confirmed or denied the relationship. The two appeared together in the National Theatre's production of The PowerBook, a play based on the novel of the same name by Jeanette Winterson, in which they played lovers.