The daughter of highly political, socialist-feminist parents, as a child Burrows sold the Socialist Worker newsletter for pocket money, attended marches and rallies after school with her activist mother and stepfather, and shared her home with striking miners. Burrows was 15 when she was discovered by the same model scout who set Naomi Campbell on the path to fame, moving to Paris to work for Chanel, Vivienne Westwood and Yves St Laurent. After five years, however, she had became so disillusioned with the fashion industry that, having studied drama since her childhood, she segued into acting. At 20 Burrows was cast in her first starring role opposite Daniel Day-Lewis in "The Name of the Father" (1993), playing his girlfriend both on and off screen. Next Burrows enticed Chris O'Donnell to cheat on Minnie Driver in "Circle of Friends" (1995), and though the movie did not launch her in quite the same way it did Driver, her career steadily gathered steam—and she also became popular fodder for the hungry British press after an engagement to actor Alan Cumming ended when he left her for a man. On screen, Burrows next appeared as a nightclub hostess in two 1996 British TV 1996 productions written by Dennis Potter, "Karaoke" and "Cold Lazarus" (both seen in the USA on Bravo in 1997), and the actress co-starred as a woman who comes between two brothers in the Australian comedy "Hotel de Love" (1997).
Burrows also starred as Janeane Garofalo's romantic competition for David O'Hara in "The Matchmaker" (1997) and was tapped for a role in Woody Allen's "Celebrity" (1998). Her strong turn as a moderately successful writer in the quirky comedy "Lovelife" (1997) was relegated to the video shelves but a bitchy bit in Mike Figgis' "One Night Stand" (also 1997) led him to cast her in a featured role as twins in "The Death and the Loss of Sexual Innocence" (1999), then quite effectively as the leading lady in his adaptation of August Strindberg's play "Miss Julie" (1999), yet again in the ensemble cast of his experimental four-way split-screen, digitally shot "Timecode" (2000), and finally as the Duchess of Malfi in his confounding film "Hotel" (2001); Figgis and Burrows were also romantically involved for several years (the actress has enjoyed relationships with both men and women).
Her first bid a mainstream Hollywood stardom came in 1999 with role as starship pilot Lt. Cmdr. 'Angel' Devereaux in the middling video game adaptation "Wing Commander" opposite Freddie Prinze, Jr., and as the oceanographer heroine of Renny Harlin's "Jaws"-on-steroids shark flick "Deep Blue Sea." She quickly returned back to artier, edgier and more high-minded fare, such as the British crime drama "Gangster No. 1" (2000) opposite Paul Bettany and Malcolm McDowall. Burrows' exotic, unreadable qualities came to the fore in director Michael Apted's "Enigma" (2001), a rather unexciting World War II thriller about the effort to crack Nazi spy codes in which she plays the lover of a code-cracker (Dougray Scott) who mysteriously disappears. In "Tempted" (2001) she plays the beautiful young wife of an older man (Burt Reynolds) who puts her fidelity to the test by hiring a younger man (Peter Facinelli) to seduce her.
Another frequent Figgis collaborator, Salma Hayek, cast Burrows in a supporting role in her highly-praised biopic "Frida" (2002), and the actress starred opposite Harvey Keitel in the little-seen drama "The Galindez File" (2003). Just as it seemed that Burrows and conventional Hollywood had significantly cooled on each other--her only mainstream role in years being the voice of the narrator in the 2003 film production of "Peter Pan"--until she was cast opposite Brad Pitt as the unfortunate Trojan princess Andromache in director Wolfgang Petersen's Homeric epic "Troy" (2004). After a supporting role in the foreign-made “Klimt” (2006), a biopic of famed Austrian artist Gustav Klimt (John Malkovich), Burrows played a mentally unstable dental patient who accuses her dentist (Don Cheadle) of sexual assault in “Reign Over Me” (2007), a touching, but ultimately flawed drama about another dentist (Adam Sandler) still devastated over the loss of his family on 9/11 five years later who runs into his college roommate (Cheadle) at a time when both could use a trusted friend in their lives.