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.
Firth has already won best actor at the Screen Actors Guild awards, the Golden Globes and the Critics' Choice Movie Awards for his portrayal of the current British monarch's father. He is nominated for best actor at the Feb. 27 Oscars.
Firth's co-stars in The King's Speech - Helena Bonham Carter and Geoffrey Rush - won the best supporting actress and actor respectively. Bonham Carter thanked the royal family in her acceptance speech.
The film also won the award for outstanding British film, music and scriptwriter David Seidler picked up the best original screenplay prize.
"Inception" picked up three awards including sound and special visual effects.
David Fincher won the best director award for "The Social Network," which tells the tale of the founding of the Facebook website. The film, which has been one of the most tipped for Oscar glory, also won the award for best adapted screenplay.
Best actor nominee Jesse Eisenberg picked up the award on Fincher's behalf as he was unable to attend due to filming.
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