While collecting the Original Screenplay for "The Favourite", Deborah Davis said: "I'm so excited to be standing here to receive my first BAFTA for my first screenplay.
"Thank you for celebrating our female-dominated movie about women in power."
Netflix's "Roma" scooped up big honours, including the Best Film, Best Director, Film Not in the English Language and Cinematography.
Cuaron won in each of these categories, setting a tone of sorts for what to expect at the Oscars later this month.
He thanked Netflix for having the "faith and courage to get behind a black-and-white film about a domestic worker, subtitled from Spanish, and bring it to audiences around the world".
"To see a film about an indigenous domestic worker embraced this way in an age when fear and anger propose to divide us means the world to me.
"Reverting back to a world of separation and isolation is not a solution to anything. It is simply an excuse to hide our fear within our basest instincts," he said.
Acting accolades went to Rami Malek for his lead role as Queen star Freddie Mercury in "Bohemian Rhapsody", which also won an award for Sound.
Mahershala Ali won the Best Supporting Actor for "Green Book", a film backed by Reliance Entertainment's Amblin Entertainment.
Diversity was celebrated as Guyanese-born British actress Letitia Wright won the EE Rising Star Award -- an honour that the public votes for.
"BlacKkKlansman" won for Adapted Screenplay, "Spider-Man: Into the Spider-Verse" took the award for Animated Film, the Best Documentary went to "Free Solo", "Vice" won for Editing, and "Black Panther" received the BAFTA for Special Visual Effects.
"A Star Is Born" won for Original Music -- an award that singer-actress Lady Gaga was ecstatic about.
The film's actor-director Bradley Cooper, who composed music for it too, said: "I got to fulfill a dream I never thought would happen, and I got to do it with some of the best musicians in the world. The music was the heartbeat of the film."
Writer-director Michael Pearce and Producer Lauren Dark received the award for Outstanding Debut by a British Writer, Director or Producer for "Beast".
The Special Award for Outstanding British Contribution to Cinema was presented to Elizabeth Karlsen and Stephen Woolley, a producing partnership who have created some iconic British films of recent years, including "The Crying Game", "Company of Wolves", "Little Voice", "Scandal", "Carol" and "Colette".
The Fellowship, the highest honour the Academy can bestow, was presented to editor Thelma Schoonmaker.
The show featured performances by Cirque du Soleil and Jess Gillam. The elegantly dressed Duke and Duchess of Cambridge took front row seats at the event.
Take a look at the full list of winners below:
Best film: ‘Roma’
Director: Alfonso Cuaron, ‘Roma’
Original Screenplay: ‘The Favourite,’ Deborah Davis, Tony McNamara
Adapted Screenplay: ‘BlacKkKlansman,’ Spike Lee, David Rabinowitz, Charlie Wachtel, Kevin Willmott
Leading actor: Rami Malek, ‘Bohemian Rhapsody’
Leading actress: Olivia Colman, ‘The Favourite’
Supporting actor: Mahershala Ali, ‘Green Book’
Supporting Actress: Rachel Weisz, ‘The Favourite’
Original music: ‘A Star is Born,’ Bradley Cooper, Lady Gaga, Lukas Nelson
Cinematography: ‘Roma,’ Alfonso Cuarón
Editing: ‘Vice,’ Hank Corwin
Production design: ‘The Favourite,’ Fiona Crombie, Alice Felton
Costume design: ‘The Favourite,’ Sandy Powell
Make up & hair: ‘The Favourite,’ Nadia Stacey
Sound: ‘Bohemian Rhapsody,’ John Casali, Tim Cavagin, Nina Hartstone, Paul Massey, John Warhurst
Special visual effects: ‘Black Panther,’ Geoffrey Baumann, Jesse James Chisholm, Craig Hammack, Dan Sudick
Film not in an English language: ‘Roma,’ Alfonso Cuarón, Gabriela Rodríguez (WINNER)
Documentary: ‘Free Solo, Elizabeth Chai Vasarhelyi, Jimmy Chin, Shannon Dill, Evan Hayes
Animated film: ‘Spider-Man: Into the Spider-Verse,’ Bob Persichetti, Peter Ramsey, Rodney Rothman, Phil Lord
Outstanding British film: ‘The Favourite,’ Yorgos Lanthimos, Ceci Dempsey, Ed Guiney, Lee Magiday, Deborah Davis, Tony McNamara
Outstanding debut by a British writer, Director or Producer: ‘Beast,’ Michael Pearce (Writer/Director), Lauren Dark (Producer)
British short animation: ‘Roughhouse,’ Jonathan Hodgson, Richard Van Den Boom
British short film: ‘73 Cows,’ Alex Lockwood
EE Rising Star Award (Voted by the Public): Letitia Wright