In the movie, Colin Firth plays Britain's King George VI, a monarch who hated public speaking because of his severe speech impediment, then took the throne in 1936 after his elder brother King Edward VIII abdicated so he could marry an American divorcee.
"The King's Speech" is about how George worked with an unconventional speech therapist, played by Geoffrey Rush, to find his voice shortly before England joined World War II. Helena Bonham Carter plays the king's supportive wife.
Firth won the BAFTA Sunday for Leading Actor, while his co-stars Rush and Bonham Carter won the awards for Supporting Actor and Actress respectively.
The film also earned honors in the Original Music and Original Screenplay categories.
Natalie Portman won the Leading Actress accolade for her portrayal of a tormented ballerina in "Black Swan."
The Facebook origins picture "The Social Network" won the prizes for Editing, Best Director for David Fincher and Best Adapted Screenplay for Aaron Sorkin.
While Firth and Portman have previously won Golden Globes, Screen Actors Guild Awards and Critics' Choice Awards this season for their respective performances in "The King's Speech" and "Black Swan," Rush and Bonham Carter were trumped in all three Hollywood races by "The Fighter" co-stars Christian Bale and Melissa Leo.