The drama won five trophies including best film, best British film and best actress for Frances McDormand.
Gary Oldman won best actor for playing Winston Churchill - one of two awards for World War Two epic Darkest Hour.
Fantasy romance The Shape of Water took three trophies, including best director for Guillermo Del Toro.
But there were few surprises among the main awards on a night when the main talking point came from the fact most guests wore black in support of the Time's Up and Me Too campaigns.
Three Billboards, set in the wake of a gruesome killing in Missouri, was written and directed by British-born Martin McDonagh.
The Bafta (British Academy Film Awards) results will strengthen its chances at the Oscars in two weeks - although Bafta's last three best films have not gone on to win best picture at the Oscars.
As well as best film, best British film and best actress, its haul included best supporting actor for Sam Rockwell and best original screenplay for McDonagh.
The Shape of Water led the Bafta nominations with 12, but came away with three - best director, production design and original music.
Other notable winners:This was Gary Oldman's first Bafta for acting - although he won for writing and directing Nil By Mouth 20 years ago Allison Janney, best known for The West Wing, won best supporting actress for I, Tonya - it was her first Bafta nomination Get Out's Daniel Kaluuya was a popular winner of the Rising Star award, and paid a heartfelt thanks to his mum in his speech At the age of 89, James Ivory - of Merchant Ivory fame - won best adapted screenplay for Call Me By Your Name Sir Ridley Scott has never won a competitive Bafta but got his third honorary award with the Bafta Fellowship (he got a "special award" in 1992 and an "outstanding contribution" in 1995)
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