The Theory of Everything was also named outstanding British film and won a third award for its adapted screenplay.
Age drama Boyhood – shot over 12 years with the same cast – was named best film, with Richard Linklater picking up best director prize.
Patricia Arquette also won the best supporting actress BAFTA for her role in Boyhood.
The ceremony at London’s Royal Opera House on Sunday night was hosted by Stephen Fry.
Julianne Moore won the leading actress prize for her performance as a linguistics professor with early-onset Alzheimer’s in Still Alice.
Wes Anderson’s comedy The Grand Budapest Hotel won the most awards on the night – a total of five including costume design, production design, make-up and original music; with Anderson winning his first BAFTA for original screenplay.
Jazz drumming drama Whiplash also took three awards – for editing, sound and supporting actor for JK Simmons, who thanked director Damien Chazelle for “the gift of this character”.
World War Two drama The Imitation Game, with Benedict Cumberbatch as codebreaker Alan Turing, won nothing despite its nine nominations.
Showbiz satire Birdman, staring Michael Keaton as a washed up superhero actor, took only one award – for Emmanuel Lubezki’s cinematography.
The obituary section also paid tribute to Robin Williams, Billie Whitelaw and Lauren Bacall – among others – who died in the past year.
The Lego Movie, which caused a shock by being snubbed by the Oscars, was named best animated film.
Unbroken actor Jack O’Connell won the Rising Star award, the only one of the awards to be voted for by the public.
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