The royal biopic, which won awards for best film, best actor and best supporting actor and actress, also leads the field at the Academy Awards with 12 nominations.
It had been nominated for 14 BAFTAs, ahead of ballet drama "Black Swan" and "Inception," starring Leonardo DiCaprio.
"To win best British film and best film at home ... it's a huge thing," director Tom Hooper told reporters.
Hooper said reports that Britain's Queen Elizabeth approved of the film and found it moving were particularly gratifying.
"The fact that it appears to have a seal of approval means a huge amount to me and Colin."
Firth picked up his second BAFTA best actor award in two years after winning the prize for "A Single Man" last year.
"This thing has run away with us all, we're all astonished," he said.
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