Glaswegian singer Capaldi took home the song of the year and best new artist awards, while Dave won the coveted album of the year gong for Psychodrama.
The pair led the nominations prior to the ceremony, with both artists securing four nominations in the same categories.
On a memorable night for south London rapper Dave, he took to the stage to perform and accused Boris Johnson of being a racist, criticised the treatment of the Duchess of Sussex and highlighted the plight of the Grenfell victims.
Labour leader Jeremy Corbyn later tweeted the lyrics from Dave's freestyle rap.
No women won any of the awards which were not gender-specific after securing just four nominations out of a possible 25 in the categories.
After picking up the male solo artist award, Stormzy paid tribute to the women in his team.
"To be the best male, I have got the most incredible females in my team," he said.
"You lot are the greatest, the best male is nothing without the best females. I love you guys.
"To every single person who supported me, I love you. Thank you guys."
It is only the fifth time best male has been won by a non-white artist.
James Bond song
The show featured performances from artists including Billie Eilish, Capaldi, Dave, Stormzy and Sir Rod Stewart.
Mabel, who won the best female artist gong, opened the show at the O2 Arena with her song Don't Call Me Up.
She said that it felt like a "full-circle" moment after her mother, musician Neneh Cherry, performed at the ceremony decades earlier.
Prior to her performance, she said on the red carpet: "It's actually 30 years since my mum performed at the Brits and it's just so amazing and such a lovely, sort of full-circle moment.
"Mainly I just feel so honoured to be here tonight, it's been such a journey".
It is the 12th time best female has been won by a non-white artist.
Other winners included Eilish, who won best international female solo artist, and Tyler, The Creator, who scooped the equivalent male award.
Eilish, who performed her new James Bond song during the ceremony, said London felt "like a second home" to her and that seeing the crowds made her emotional.
"I have felt very hated recently," she said.
"When I was on stage and I saw you guys all smiling at me it genuinely made me want to cry and I want to cry now."
After picking up his award Tyler, The Creator made fun of former prime minister Theresa May, who he said had previously stopped him entering the country.
He said: "Thank you Theresa May.
"I know she's at home p***** off."
Caroline Flack tribute
The ceremony, which was celebrating its 40th anniversary and hosted by Jack Whitehall, opened with a tribute to the late former Love Island host Caroline Flack, who was found dead on Saturday having taken her own life.
Whitehall said she was "a member of the Brits family" during his opening monologue, adding that she was "a kind and vibrant person with an infectious sense of fun".