The movie, chronicling a grieving mothers campaign for justice, won for original screenplay and outstanding British film, while Frances McDormand bagged best actress and Sam Rockwell best supporting actor prizes.
"The Shape of Water" -- the most heavily nominated film of the night with 12 nods -- came away with only three awards, including best director for Guillermo Del Toro, while "Darkest Hour" claimed two prizes, including for Gary Oldman as best actor.
"Our film is a hopeful one in lots of ways but its also an angry one," Martin McDonagh, writer and director of "Three Billboards", said in his acceptance speech.
"And as weve seen this year, sometimes anger is the only way to get people to listen and to change, so were thrilled that Bafta has recognised this."
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Star's arrived at Londons Royal Albert Hall predominantly dressed in black in solidarity with the #MeToo and "Times Up" campaigns, mirroring other recent American red carpets including last months Golden Globes.
British royals avoid making overtly political statements or gestures, so there was little surprise when the Duchess of Cambridge chose to wear a dark green dress, by British designer Jenny Packham, as she accompanied husband Prince William, president of Bafta, to the ceremony.
Jane Lush, chair of Bafta, opened the evening soberly telling the star-studded audience it was important to acknowledge a "difficult" past year, and noted efforts to tackle gender inequality.
"Brave revelations have followed brave revelations of bullying and sexual harassment, and which to all our shame has been hidden in plain sight for decades," she said.
Host Joanna Lumley, a British film and TV star, also praised the gender equality movement as a continuation of the work of the Suffragettes a century ago.
She hailed the "determination to eradicate the abuse of women the world over" as she took to the stage.
Meanwhile in an open letter published before the awards, almost 200 British and Irish stars backed a new fund to help women facing sexual harassment and abuse at work.
It echoes a similar initiative launched in Hollywood last month, and was kick-started with a USD 1.4 million donation from actress and activist Emma Watson.
"The Shape of Water", a story of love between a mute cleaning woman and a mystery merman-like creature, led the pack just as it has across the Atlantic, where it has topped the list of Oscar nominations with 13 nods, including for best picture.
As well as director del Toros award for direction, composer Alexandre Desplat collected the original music award -- his third BAFTA win -- and the film also won best production design.
Allison Janney won best supporting actress for her role as the mother of controversial figure skater Tonya Harding in biopic "I, Tonya".
Gary Oldman's turn as Churchill in "Darkest Hour" has so far won him a Golden Globe, a Bafta and the chance of an Oscar on March 4.
He paid tribute to the wartime British leader, saying: "In those dark, uncertain days in 1940, he held the line for honour, for integrity and freedom for his nation and the world, so I thank you, Sir Winston."
Accepting her best actress accolade, McDormand, who chose not to wear black, quoted her on-screen character who has "a little trouble with compliance".
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