La La Land has dominated the Baftas, taking five trophies – including best film and best actress for Emma Stone.
There were also awards for Lion, including best supporting actor for Dev Patel, and Ken Loach’s I, Daniel Blake, which was named outstanding British film at the London ceremony.
Patel said the win was “overwhelming”.
Casey Affleck was named best actor for Manchester by the Sea and Viola Davis won the best supporting actress prize for Fences.
She is also nominated for an Oscar for her role in Fences, based on the August Wilson stage play of the same name.
Manchester by the Sea also won the best original screenplay, for the text by its director Kenneth Lonergan.
You may well be tired of hearing about La La Land, but its winning streak shows no signs of slowing down.
The recognition by Bafta is a good sign for the musical – also starring Ryan Gosling – coming just weeks before the Oscars. It had been nominated for 11 Baftas in all and is in contention for 14 Academy Awards.
La La Land has already smashed the record for the most Golden Globes, winning seven prizes last month
Stone was among the winners to make an oblique reference to world affairs, although the new US President Donald Trump was not explicitly mentioned during the acceptance speeches.
After thanking La La Land’s director Damien Chazelle, who took home the best director statuette, Stone told the audience: “This country – and the US, and the world – seems to be going through a bit of a time, just a bit.
“In a time that’s so divisive, I think it’s so special we were able to come together tonight thanks to Bafta, to celebrate the positive gift of creativity and how it can transcend borders and how it can help people to feel a little less alone.”
She beat Meryl Streep, Amy Adams, Emily Blunt and Natalie Portman, and is also in the running for an Academy Award.
Affleck, who plays a grieving handyman in gritty drama Manchester by the Sea, seemed taken aback by his win, saying: “The room looks very different from here. My heart is beating.”
After the awards, he said he had spoken to Meryl Streep backstage about her recent Donald Trump speech.
Affleck said: “I told her how much her speech at the Golden Globes meant to all of us and how grateful I was that she did it and kicked in the door a little bit, and said it’s OK to talk about these things and said it doesn’t matter if we are actors, we have been given a microphone and we can speak out.
“She said, ‘I think there is hope around the corner’.”