The period drama, which was partially filmed at the National Trust property Knole park in Sevenoaks, also picked up gongs for best British film, costume design, original screenplay, make-up and hair and production design.
Australian Margot Robbie missed out, however, on an award for best supporting actress for her performance as Queen Elizabeth I in Mary Queen of Scots.
The Absolutely Fabulous star began the British film awards ceremony on Sunday night with a series of gags about the nominated films and stars, but some viewers were shocked at her quip about the film BlacKkKlansman.
Netflix film Roma scooped top prize at the British Academy of Film and Television Arts (BAFTA) on Sunday.
Elsewhere, Roma, Alfonso Cuaron's black-and-white film about his childhood in Mexico City, was named best film and best film not in the English language, while he was also named best director and cinematographer.
"I am seriously touched this film has been received the way it has been received", the 57-year-old filmmaker said while receiving his BAFTA for best director.
Paul Pogba's individual highlights have emerged from Fulham 0-3 Man Utd
The brace took Pogba's tally to 11 goals this season, a milestone he has only achieved for the first time in his career. Pogba has netted eight times and has made five assists in 10 games since Mourinho left the Old Trafford outfit.
"Reverting back to a world of separation and isolation is not a solution to anything", Cuaron added.
"As far as I'm concerned, all three of us are the same and should be the lead.This is for all three of us".
"We're having an fantastic night aren't we", Colman told her fellow "The Favourite" nominees as she picked up the award.
Colman - who rose to fame playing Sophie Chapman in Peep Show - paid tribute to her "classiest and coolest" fellow co-stars in the film, Rachel Weisz and Emma Stone, and said in her eyes, the award was for all three of them as leads, and that she would "scratch in" their names on the Bafta statuette too. We're going to get so pissed later. "It's got my name on it, but we can scatch some other names on".
In his acceptance speech, Malek thanked the late Queen's frontman as "the greatest outsider of them all".
A Star is Born won the prize for best original music, accepted by the film's writer, director and star, Bradley Cooper.