The movie also picked up the prizes for Best Original Screenplay, Cinematography, Music and Costume Design at Sunday's awards ceremony, while star Jean Dujardin was named Best Actor and Michel Hazanavicius went home with the Best Director trophy.
The Cold War-era spy thriller "Tinker Tailor Soldier Spy" won the awards for Best British Film and Best Adapted Screenplay.
Meryl Streep was named Best Actress for her work in "The Iron Lady," and Christopher Plummer and Octavia Spencer won matching Supporting Actor and Actress BAFTA masks for their respective work in "Beginners" and "The Help."
The BAFTAs were handed out at the Royal Opera House in London's Covent Garden. Comedian, actor and author Stephen Fry served as host of the ceremony.