The trophies for Sir Sam Mendes's movie included best film, best British film, best director and best cinematography.
Joker won three awards including best actor for Joaquin Phoenix, while Renee Zellweger was named best actress for her portrayal of Judy Garland.
Phoenix took aim at "systemic racism" and "oppression" within the film industry in his acceptance speech.
His words, and those of the Duke of Cambridge later, came in the wake of a diversity row prompted by the all-white line-up of acting nominees.
South Korean film Parasite won two prizes - for original screenplay and film not in the English language.
There were no major upsets or surprise winners, with 1917 unarguably dominating the evening.
"I couldn't be more thrilled," director Sir Sam told BBC News backstage. "There's the personal delight in seeing a story very close to me and my family be developed and enlarged but the massive thing has been audiences going in large numbers. Sir Sam is the first British winner of best director at the Baftas since Danny Boyle won for Slumdog Millionaire in 2009.
Brad Pitt won best supporting actor for his role in Quentin Tarantino's Once Upon A Time In Hollywood and made a Brexit joke in a message read out by his co-star Margot Robbie.
"Hey, Britain, hear you've become single - welcome to the club! Wishing you the best with the divorce settlement," the actress read. Laura Dern was named best supporting actress for her performance as a divorce lawyer in Marriage Story.
It is the first time since 1977 that all four of the Bafta awards for acting have been won by Americans.
Accepting the leading actress award for her performance in Judy, Zellweger said: "This is very humbling. Miss Garland, London town, which you have always loved so much, still loves you back. This is for you."
Netflix's festive animation Klaus won best animation, beating big hitters like Toy Story 4 and Frozen 2.
Micheal Ward, star of Top Boy and Blue Story, was named the Bafta rising star.
Andy Serkis was honoured with the outstanding British contribution to film award, presented to him by Sir Ian McKellen. —BBC
