12 Years A Slave, which was directed by Steve McQueen, was crowned Best Film at the awards at the Royal Opera House, London, while its star Chiwetel Ejiofor was named Best Actor.
Ejiofor, 36, was presented with his award by Uma Thurman - who looked sensational in a simple black Atelier Versace dress - and said he was "so deeply honoured and privileged to receive it". He thanked McQueen for his "artistry and passion".
McQueen, accepting his award, told the audience: "There are 21 million people in slavery as we sit here. I just hope 150 years from now our ambivalence will not allow another film-maker to make this film".
The A listers had gathered in Covent Garden for the 67th annual event, which was hosted by actor Stephen Fry.
Among the guests was the Duke Of Cambridge, who presented the Fellowship award to Dame Helen Mirren. Before presenting the Fellowship to her, the Prince William described her as "an extremely talented British actress who I should probably call granny".
Gravity, which features US stars Sandra Bullock and George Clooney, had been nominated in 11 categories and lifted six prizes.
As well as Best British Film, it took the awards for Best Sound, Original Music, Visual Effects and Cinematography. The film's director Alfonso Cuaron was also named Best Director.
Gravity caused some controversy by being listed as a British film, but it was filmed in this country and the team responsible for its visual effects are UK-based.
Cate Blanchett won Best Actress for her role in the Woody Allen film Blue Jasmine. She dedicated her win to actor Philip Seymour Hoffman, who died earlier this month.
Emma Thompson presented the award for Best Supporting Actor to Barkhad Abdi for his role as a Somalian pirate in Captain Phillips.
The Best Supporting Actress gong was given to Jennifer Lawrence for American Hustle, with the film's director, David O Russell, accepting it on her behalf.
The award for Best Original Screenplay also went to American Hustle.
The Bafta for Production Design went to the adaptation of F Scott Fitzgerald's classic American novel The Great Gatsby.
The Best Editing award went to Rush, while The Act Of Killing - about Indonesian death squads who murdered thousands in the 1960s - won Best Documentary.
Awards for Make-Up and Hair and Costume Design went to American Hustle and The Great Gatsby respectively.
Comedian and actor Steve Coogan presented the Bafta for Outstanding British Debut to Kieran Evans for his film Kelly + Victor.
Film-maker Peter Greenaway, whose career includes art-house hits such as The Cook, The Thief, His Wife and Her Lover, was then presented with the Outstanding Contribution Award by Juliet Stevenson.
Coogan and Jeff Pope then won the award for adapted screenplay for Philomena, the story of an Irish woman's search for the son she was forced to give up for adoption. Earlier in the evening fans lined the red carpet to catch a glimpse of celebrities including Amy Adams, Leonardo DiCaprio and Martin Scorsese.
Among the stars pulling out all the stops were Brad Pitt and Angelina Jolie, who wore matching tuxedos.
Pop star Lily Allen brought a rush of colour to the ceremony as she posed in an orange and pink dress with an eccentric headpiece.