The war thriller also won prizes for original screenplay, cinematography, editing, and sound during the ceremony at London's Royal Opera House.
Accepting her award for Best Director, Bigelow said, "What an honour, especially to be in this room filled with so many incredibly talented people that I've admired and been inspired by for decades."
Colin Firth saw off Jeff Bridges (Crazy Heart), George Clooney (Up In The Air), Jeremy Renner (The Hurt Locker) and Andy Serkis (Sex & Drugs & Rock & Roll) to win the Leading Actor title for his role in Tom Ford's directorial debut, A Single Man.
Firth paid tribute to Ford while picking up the trophy, saying, "I think an encounter with Tom Ford is to come away resuscitated, a little more worldly, better informed, better groomed, more fragrant and more nominated than one has ever been before. I've worked with a lot of great directors and he's definitely up there with the very best of them."
Carey Mulligan scooped Leading Actress for An Education, triumphing over Hollywood veteran Meryl Streep (Julie & Julia), French star Audrey Tautou (Coco Before Chanel), Saoirse Ronan (The Lovely Bones), and Gabourey Sidibe (Precious: Based on the Novel Push by Sapphire).
Mulligan was shocked at her award, saying, "I didn't expect this at all so I didn't think of anything to say. Thank you so much. BAFTA, that's just... I was a here a year ago and I just never imagined in a million years..."
Christoph Waltz was awarded Supporting Actor for his role in Quentin Tarantino's Inglourious Basterds, and Mo'Nique was named Supporting Actress for her part in Precious: Based on the Novel Push by Sapphire.
Twilight star Kristen Stewart picked up the Orange Rising Star Award - the only prize to be voted for by the public - and veteran actress Vanessa Redgrave received the BAFTA Fellowship honour to mark her notable career.
The list of winners is as follows:
Best Film - The Hurt Locker
Director - Kathryn Bigelow, The Hurt Locker
Leading Actor - Colin Firth, A Single Man
Leading Actress - Carey Mulligan, An Education
Outstanding debut by a U.K. filmmaker - Duncan Jones, Moon
Outstanding British Film - Fish Tank
Supporting Actor - Christoph Waltz, Inglourious Basterds
Supporting Actress - Mo'nique, Precious: Based on the Novel Push by Sapphire
Animated Film - Up
Adapted Screenplay - Up In The Air
Orange Rising Star Award - Kristen Stewart
Special Visual Effects - Avatar
Original Screenplay - The Hurt Locker
Production Design - Avatar
Film Not In The English Language - A Prophet
Sound - The Hurt Locker
Editing - The Hurt Locker
Cinematography - The Hurt Locker
Fellowship - Vanessa Redgrave