Gravity has been named best British film at the Baftas.
It was also honoured for visual effects, cinematography, best sound and original music. Alfonso Cuaron also won best director.
12 Years a Slave won best film with its star Chiwetel Ejiofor winning best actor while Cate Blanchett picked up best actress for Blue Jasmine.
In the supporting categories, Captain Phillips star Barkhad Abdi won as did Jennifer Lawrence for American Hustle.
The actress was not at the ceremony with director David O Russell accepting the award instead.
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.
Director Steve McQueen accepted the best film award for 12 Years. The filmmaker thanked his “one and only mother for having the faith. Never give up”.
Ejiofor, who seven years ago won the Bafta rising star award, accepted his award from US actress Uma Thurman.
He said he was “so deeply honoured and privileged to receive it”, thanking McQueen for his “artistry and passion”.
He joked: “This is yours, by the way, I know that, you know that. I’m going to keep it but it’s yours”.
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 were 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.
US director 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.
Coogan praised the “real Philomena Lee”, adding that “her story has been told and her story finished in the Vatican. She has been heard but there are 60,000 women who are yet to trace their children”.
She may have lost out to Blanchett but Dame Judi set a Bafta record with her 15th acting nomination.
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.”
Blanchett paid tribute on stage to the late actor Philip Seymour Hoffman, who died earlier this month in New York, calling him “a continual profound touchstone”.
She added: “Phil, buddy, this is for you, you bastard. I hope you’re proud.”
The Baftas can be an indicator of which films go on to win Academy Awards two weeks later.
Last year Argo won best film, Daniel Day-Lewis won best actor, and Christoph Waltz and Anne Hathaway took the best supporting acting prizes. They all went on to win Oscars.
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 Dame Helen Mirren with the British Academy fellowship, its highest accolade.
Previous winners have included Charlie Chaplin, Alfred Hitchcock, Steven Spielberg and Stanley Kubrick.
Dame Helen paid tribute to her drama teacher Alice Welding, who died recently at the age of 102.
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 Millers accepting the award.