Rachel Weisz had earlier picked up the prize for Best Supporting Actress for her role as the Duchess Of Malborough, while it also scooped the award for Outstanding British Film. Malek, who called his win "truly extraordinary", did express his gratitude to Dexter Fletcher, who stepped in for Singer but is not a credited director on the film.
Alfonso Cuaron's semi-autobiographical film, about a domestic worker in 1970s Mexico, has won a string of prizes this awards season, further cementing its path to potential Oscar success.
It won out against "Lord of the Rings" director Peter Jackson´s "They Shall Not Grow Old" in which silent black-and-white footage from World War I was transformed into a 3D colour movie.
"The thing I really want to do is, Emma and Rachel (must keep this together) not just for your performances but for what you did after the cameras stopped rolling".
This year's leading actress category is similarly competitive, featuring Glenn Close for "The Wife", Lady Gaga for "A Star Is Born", Melissa McCarthy for "Can You Ever Forgive Me?", Olivia Colman for "The Favourite" and Viola Davis for "Widows".
Rachel Weisz poses for photographers backstage with her Best Supporting Actress award for her role in the film The Favourite.
"We're having an wonderful night". We are going to get so pissed later.
Colman then briefly lost her point but then added: "This isn't for the lead it's for A lead and as far as I'm concerned all three of us are the same and should be the lead and it's weird that we can't do that". It's got my name on it but we can scratch in some others. He paid tribute to Mercury in his acceptance speech.
Colman thanked her co-stars Weisz and Emma Stone while accepting the award at London's Royal Albert Hall on Sunday evening, United Kingdom time. Presenters also included Prince William, who has served as president of BAFTA since 2010.
BlackKklansman won the prize for Best Adapted Screenplay and Spider-Man: Into the Spider-Verse scored the Best Animated Film trophy.
Rami Malek won leading actor for "Bohemian Rhapsody", and Mahershala Ali won supporting actor for "Green Book".