Cate Blanchett was not at the ceremony with director David O. Russell accepting the award instead.
David O. Russell was back on stage minutes later to pick up the award for best original screenplay for the 1970s crime drama, about two con artists who get entangled with the FBI.
In the supporting categories, Captain Phillips star Barkhad Abdi won as did Jennifer Lawrence for American Hustle.
Gravity has been named best British film.
It was also honored for visual effects, cinematography, best sound and original music. Alfonso Cuaron also won best director.
The Great Gatsby picked up two awards for production design and costume design.
Room 8 was named best short film; the short animation award was won by Sleeping With the Fishes.
The awards are being hosted for a ninth time by actor Stephen Fry.
Best animation went to Frozen, which came out ahead of Monsters University and Despicable Me 2.
The BAFTA for outstanding debut by a British writer, director or producer went to Kieran Evans for Kelly + Victor, the tale of a young couple embarking on a passionate love affair.
Ron Howard, whose film Rush – about the rivalry between F1 drivers James Hunt and Niki Lauda – won the award for best editing, joked on the red carpet he felt like “a grateful foreign exchange student”.
Steve Coogan and Jeff Pope won for their adapted screenplay for the film Philomena, based on the true story of an Irish woman trying to find the son she was forced to give up for adoption.
She may have lost out to Cate Blanchett but Judi Dench set a BAFTA record with her 15th acting nomination but when asked about it on the red carpet, she replied: “I didn’t know until you told me. Thanks for reminding me.”
She added: “It means I’ve been gong for a very, very long time.”
The BAFTAs can be an indicator of which films go on to win Academy Awards two weeks later.
Presenters and guests included Eddie Redmayne, Jeremy Irons, Maggie Gyllenhaal, Stanley Tucci and Uma Thurman.
The ceremony opened with a duet from Tinie Tempah and Mercury Prize nominee Laura Mvula.
Prince William, the academy’s president, presented Helen Mirren with the British Academy fellowship, its highest accolade.
Previous winners have included Charlie Chaplin, Alfred Hitchcock, Steven Spielberg and Stanley Kubrick.
Peter Greenaway also received the outstanding British contribution to cinema award, presented by Juliet Stevenson.
The winner of the public vote for this year’s Rising Star award was also announced with 21-year-old British actor Will Poulter from We’re the Miller accepting the award.
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