The movie's novice feature film-maker Stephen Daldry won the best director category and its star, 14-year-old Jamie Bell, took best newcomer.
The emotional story of a miner's son who overcomes adversity to become a top ballet dancer took gongs for best British independent film and best screenplay.
The movie's novice feature film-maker Stephen Daldry won the best director category and its star, 14-year-old Jamie Bell, took best newcomer.
The annual ceremony at the Cafe Royal in London marks the culmination of the two-week Raindance Independent Film Festival.
Awards are given in 11 categories with the aim of celebrating merit and achievement in independently funded British film-making.
But there are also titles handed out to honour talent in the foreign independent film industry.
Billy Elliot was released this month but is fast becoming one of this year's most successful films, winning strong praise in both the UK and the US.
International success
After picking up the awards for the film, director Stephen Daldry said: "It's still a total joy that people are enjoying the film - that's a total surprise.
Young star Jamie Bell was unable to attend the ceremony as he is promoting the film in the US, where it has just opened.
However he sent a video message of himself jokily attracting interest for the film by standing on a New York street holding a cardboard sign with "Billy Elliot" scrawled on it.
American actress Gillian Anderson, best known for her role as agent Scully in hit TV series the X-Files, took best actress for her role in House of Mirth.
In the movie - adapted from Edith Wharton's turn-of-the-century novel - she plays New York socialite Lily Bart who waits too long for her true love to propose, played by Eric Stoltz.
Documentary award
This year's Oscar-winning documentary feature One Day in September was also honoured at the Bifa, netting its director, Kevin Macdonald, the Douglas Hickox award for British directorial debut.
The film tells the story of the hostage crisis at the 1972 Munich Olympics. The games were interrupted by Palestinian terrorists who took Israeli athletes captive.
The film includes footage taken at the time and interviews with surviving terrorist Jamal Al Gashey and various officials detailing how the police bungled the operation.
Best foreign independent in English went to Oscar-nominated The Straight Story, whose star Richard Farnsworth recently died in an apparent suicide.
Farnsworth, 80, had been diagnosed as suffering from terminal cancer.
Israeli movie Kadosh took the best independent foreign language film category.
Shot largely in an ultra-orthodox Jewish community in Jerusalem, the film examines the lives of two sisters confined to their religious community, and how they try to come to terms with their lives. One rebels, while one settles into the community.
The Raindance festival closes on 26 October with the movie It Was An Accident, starring Thandie Newton and Max Beesley.
The full list of winners is as follows: