The Broadchurch star beat Glenn Close, Lady Gaga, Melissa McCarthy and Viola Davis to win the leading actress prize for her turn as a cantankerous Queen Anne in the spiky period drama.
The movie was also named outstanding British film, with Rachel Weisz taking the best supporting actress prize, beating her co-star Emma Stone in the category.
The film had led the nominations ahead of the ceremony, with 12 nods.
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.
Cuaron thanked Bafta and Netflix for “having the courage” to get behind the film.
He said the extent to which the film has been embraced “in an age where fear and anger are proposed to divide us means the world to me”.
He said that “retreating” was not a solution and spoke about how we are all connected, adding: “And when we finally chose to embrace that connection and show compassion to one another... I believe cinema has the power to help us achieve that”.
Taking to the stage after her name was called, Colman admitted, “I’m very shaky, sorry”, and told the crowd she could not read her notes, before adding she thanked “all the producers, obvs”.
Addressing the other winners from The Favourite, she said: “We are having an amazing night, aren’t we? We are going to get so pissed later.”
Speaking about Weisz and Stone, Colman said: “As far as I’m concerned, all three of us are the same and should be the leads and it’s weird we can’t do that.
“This is for all three of us. It’s got my name on it but we can scratch on some other ones.”
The film also received accolades for its costume design, production design, make-up and hair, as well as for its original screenplay.
Rami Malek scooped the leading actor category for his turn as Freddie Mercury in Bohemian Rhapsody, while Mahershala Ali was named best supporting actor for Green Book, beating British favourite Richard E Grant in Can You Ever Forgive Me?
There was also success for British actress and Black Panther star Letitia Wright, who won the EE Rising Star award, the only Bafta voted for by the public.
Appearing overwhelmed as she collected her gong, she said: “I identify myself as a child of God and I can’t get up here without thanking God.
“A few years ago I saw myself in a deep state of depression and I wanted to quit acting. The only thing that pretty much pulled me out of that was God, my belief, my faith and my family and an email from Bafta saying they wanted me to be a part of the Bafta Breakthrough Brits and I was like, ‘Let me try again’.
“So this wasn’t an overnight thing, it wasn’t a click-of-a-finger success and I’m still a work in progress.”
She continued: “I want to encourage young people, actually you can be any age actually, I want to encourage you... anyone who has lost their light, I want to encourage you. God made you and you are important... I want to say God loves you and let your light shine.”
A Star Is Born won for its original music, with the film’s writer, director, star and composer Bradley Cooper collecting the prize.
He thanked his co-star and fellow composer Lady Gaga and the other musicians who helped with the film soundtrack before saying: “Most of all I have to thank Irina [Shayk, his partner] for putting up with me for all the music I was trying to make in our basement for a year.”
The animation category was won by Spider-Man: Into The Spider-Verse, while Free Solo, a film about the first person to climb El Capitan in Yosemite National Park without ropes, was named best documentary.
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.