Accepting her award, she said: "I'm so sorry I can't speak French. I want to thank Gary Oldman for being such a wonderful director for us. I feel silly receiving this because it was such an ensemble piece."
Burke plays the down-trodden wife of a vicious alcoholic in the grimly realistic film set in Bermondsey, south-east London. She had no idea she was going to win the award and had to fly over from Britain this afternoon where she is filming Tom Jones for the BBC.
She said: "I got a call from Gary Oldman at 1pm today telling me to get over here. I jumped on an aeroplane and a helicopter. This is all a bit strange.
Asked what it is like to go from Waynetta Slob to winning at Cannes, she said: "It's not much different really. But this is beyond my wildest dreams."
The festival's top prize, the Golden Palm for best film, was awarded jointly to the Japanese director, Shohei Imamura, for The Eel, and Abbas Kiarostami, the Iranian director for The Taste of the Cherry, a surprise decision.
Most critics had seen no outright favourite for the prize, which was awarded by the jury. Its president, the French actress Isabelle Adjani, announced a special 50th anniversary prize, awarded to Egypt's Youssef Chahine for all his work. The Sweet Hereafter, by Canada's Atom Egoyan, won a runner-up Grand Jury Prize. Sean Penn was voted best actor for She's so Lovely, by fellow American Nick Cassavetes.
But the critics weren't impressed. Michel Ciment, who edits the French film magazine Positif, said: "Quality-wise this year has been very average. Just a few years ago, and even more so 20 years ago, there was a masterpiece a day at the festival."
"What is serious this year is that there were no major discoveries, no one like Wim Wenders for example," Mr Ciment said. "This year there was too much of an emphasis on stars. There were much better films for the competition than Johnny Depp's The Brave, but organisers wanted him and possibly Marlon Brando so it got in," he said.
ernational and Moving Pictures had put Ang Lee's The Ice Storm, about a New York suburban family, and Curtis Hanson's fast-paced thriller, LA Confidential, in a narrow lead.
Outsiders also tipped by Cannes critics to pick up big prizes included Oldman's partly-autobiographical Nil By Mouth, and Michael Winterbottom's Welcome To Sarajevo, about a television journalist's adoption of a Bosnian child.
Mr Ciment opted for Egoyan's film because it "is very rich and complex, and because it's his seventh film and he's at the stage where he needs a major reward".
Violence in many films - sci-fi in the French director Luc Besson's The Fifth Element, or wife-beating in Oldman's movie, among others - dampened birthday celebrations.