Raised in Islington by her widower father and two older brothers, Burke found an escape in acting. While studying at the renowned Anna Scher Theatre School while in her teens, she was spotted by director Mai Zetterling who cast her in "Scrubbers" (1982), Around the same time, Burke penned her first play, "Mr. Thomas", about a closeted homosexual, and its 1990 professional production not only marked her own directing debut but also her first collaboration with actor Ray Winstone. By then, the actress had also appeared in three films helmed by Alex Cox: "Sid and Nancy" (1986), the nearly unwatchable "Straight to Hell" and "Walker" (both 1987).
While the 1980s had proven relatively fallow, the 90s marked her ascencion to TV stardom in England. As the decade dawned, Burke was tapped to join the variety program "Harry Enfield and Chums" and over the course of three seasons created several memorable characters, most notably the proletarian housewife Waynetta Slob, Lulu, the sniveling baby sister of Enfield's nasty toddler Harry, and the gormless male teen Perry (sidekick to Enfield's Kevin). She went on to create the recurring role of Magda, a hard-bitten magazine editor, on the popular "Absolutely Fabulous" (1994-96) and demonstrated her prodigious dramatic talents with an award-winning turn as a mute, bald woman sent to live with a Messianic preacher in the miniseries "Mr. Wroe's Virgins" (1993).
Those who were aware of the actress' gifts weren't surprised when she delivered a star-making turn as a lower-class abused housewife in Gary Oldman's semi-autobiographical directorial debut "Nil by Mouth" (1997). Teamed with Ray Winstone as her brutish husband, Burke was heartbreaking as the pregnant Val, a woman struggling to maintain her family unit despite her spouse's beatings. It was a tour de force role and the actress was more than capable of displaying the intense emotions which the role required.
Although offers from America arrived, Burke opted to remain in England. She offered a memorable cameo as Queen Mary in the biopic "Elizabeth" (1998) and held her own amidst the formidable ensemble (including Meryl Streep, Brid Brennan and Catherine McCormack) playing Maggie, the somewhat slow sister in an Irish family in "Dancing at Lughnasa" (also 1998). She followed with a turn as a romantically accommodating pub singer in "This Year's Love" (1999) and reprised her TV creation alongside Enfield in the big screen comedy "Kevin and Perry Go Large" (2000).
Burke also developed a secondary career as a stage director, helming the 1995 premiere of Jonathan Harvey's play "Boom-Bang-a-Bang". The writer was so impressed he specifically created the role of Linda, a fright-wigged woman rooming with a gay man in "Gimme, Gimme. Gimme" (1999- ). Burke further repayed him by staging his play "Out in the Open" (2001).