Hathaway, also a nominee at the Oscars, said she was "overjoyed" to win the best supporting BAFTA.
While accepting the trophy from presenter George Clooney, Hathaway said, "What am I thinking? I almost walked past George Clooney without hugging him. That's just stupid." She thanked the cast and fellow co-star Hugh Jackman.
The 23rd James Bond movie 'Skyfall' was named the British film and won in the best music category.
Bigelow's Osama bin Laden hunt thriller was the big loser at the BAFTAs as it came empty handed despite five nominations.
Quentin Tarantino won the original screenplay award for his violent, civil-war slave-revenge drama 'Django Unchained' while actor Christoph Waltz was named best supporting actor for his role of a bounty hunter.
Waltz, who won an Oscar for last Tarantino film 'Inglourious Basterds' and is nominated for a second time in the same category, credited his director for the BAFTA win.
"Why I get to stand here is really no mystery because it says so at the beginning of our movie: 'written and directed by Quentin Tarantino'," he said before thanking other cast and crew members.
"...I need and want to thank you for the thing that touches me the most, your unconditional trust... You silver-penned devil, you."
Tarantino, meanwhile, revealed plans about another film in the series while thanking his actors Waltz and Jamie Foxx for doing "a bang up job with my dialogue."
Writer-director David O Russell won the adapted screenplay prize for 'Silver Linings Playbook', which stars Indian actor Anupam Kher in a key role.
'Brave' won the best animated film while best documentary trophy went to 'Searching for Suger Man'. Best short film trophy went to 'Swimmer', short animation to 'The Making of Longbird'.
Joe Wright's 'Anna Karenina' won in the best costume design. Best Rising star award was given to Juno Temple.
Outstanding debut by a British writer, director or producer went to Bart Layton (director), Dimitri Doganis (producer) for 'The Imposter'
Director Alan Parker received a BAFTA Fellowship, Sunday night's highest honor, for his illustrious career that includes films like 'Midnight Express', 'Fame' and 'Mississippi Burning.'