Cuaron was also named best director at Sunday night's awards ceremony in London.
Welcoming the movie's director Spike Lee and star Adam Driver to the ceremony, Lumley said: "It's an incredible film, it has already won many awards". I've actually written something down.
Colman thanked her co-stars Weisz and Emma Stone in her acceptance speech, for which she used notes to try and get to the end of it without being too overcome by emotion. And Fox. Nadia [Stacey] and Sandy [Powell] and all of your teams.
"We're having an wonderful night aren't we", Colman told her fellow "The Favourite" nominees as she picked up the award.
"The thing I really want to do is Emma and Rachel-I must keep it together-not just for your performances but for what you did after the cameras stopped rolling", Colman said.
She continued: "We've never talked about this and I find it very emotional but you were the classiest and coolest honour guards any woman could ever have and I love you". Sorry, I swear I'm going to go in a minute! As far as I'm concerned, all three of us are the same and should be the lead. "It's got my name on it, but we can scratch in some other names".
"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. Leading this year's nominations is Yorgo Lanthimos' "The Favourite" with 12 nods, followed by popular films "A Star Is Born", "BlackKklansman" and "Green Book".
"Roma" is also nominated for best picture at the Oscars later this month, which has propelled Netflix into the Hollywood club of elite filmmakers despite fears that its streaming business model could undermine the industry.
Costume romp The Favourite was the biggest victor at the BAFTAs on Sunday, taking seven awards, but Netflix's black and white film Roma picked up the Best Film prize, as well as Director, at Britain's top movie honors.
A Star Is Born won for its original music, with the film's writer, director, star and composer Bradley Cooper collecting the prize.