"Roma" won the best film and best director, sharing the glory with British black comedy "The Favourite" which picked up best actress for Olivia Colman as Queen Anne and best-supporting actress for Rachel Weisz playing her confidante and lover.
Alfonso Cuaron's "Roma", which centers on the nanny to a middle-class Mexico City family, took prizes for best picture, director, cinematography and foreign-language film.
Winners relished the symbolism of their victories.
Cuaron thanked Netflix for getting behind the film, which is in Spanish and has garnered 10 Oscar nominations, a major recognition for the streaming service.
The success of the film "in an age where fear and anger are proposed to divide us means the world to me", he said.
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". It's weird. but this is for all three of us. "It's got my name on it, but we can scratch in some other names".
Mahershala Ali took the Supporting Actor prize for his role in Green Book, set in the segregated U.S. South in the early 1960s.
Spike Lee's BlacKkKlansman, based on retired American policeman Ron Stallworth's autobiographical Black Klansman, won the Best Adapted Screenplay award (Lee, David Rabinowitz, Charlie Wachtel, and Kevin Willmott).
The awards, known as BAFTAs, will be scoured for clues on who might triumph at Hollywood's Academy Awards on February 24.
The main difference with the Oscars is that at the British awards, real royalty mixes with the Hollywood variety.
"Absolutely Fabulous" star Joanna Lumley was the gently risque host.
Film editor Thelma Schoonmaker, who has made 23 films with Martin Scorsese, received the Fellowship, the Academy's highest honour, from the Duke of Cambridge at the end of the ceremony. Best British short film was "73 Cows", while Vice won the best editing. It had a single BAFTA nomination, for visual effects, which it won. The London-raised actress spoke of her own past struggles with depression and urged others not to give up.
The red carpet glamour unfolded against a backdrop of soul-searching and scandal about abuses in the entertainment industry.
BAFTA said the alleged abuse was "completely unacceptable" and incompatible with its values. There was no mention of Singer, who denies sex assault allegations that caused his nomination to be suspended.
Weisz and Stone are also in the running for Oscars in a proud year for the British film industry. He has also been nominated in the Best Actor category at the Academy Awards. The film also won the Sound prize.
BAFTA chairwoman Pippa Harris said only 10 percent of films entered for this year's awards were directed by women.
Rachel Weisz poses for photographers backstage with her Best Supporting Actress award for her role in the film The Favourite. "Men seem to find that transition much easier".