The TV superstar was crowned best leading actress after also winning best minis-series for writing and directing the hit show.
Gongs were handed out in front of a live but socially distanced audience of nominees at Television Centre in west London during Sunday’s ceremony.
The Black Lives Matter routine won the only award voted for by the public, the must-see moment.
During the performance, a man in a police uniform kneels on Banjo, echoing the killing of unarmed black man George Floyd, sparking more than 24,000 complaints to Ofcom.
But the TV watchdog dismissed the complaints, concluding that the routine’s “central message was a call for social cohesion and unity”.
Banjo and his brother Jordan covered their faces in their hands as it was announced the dance troupe had won.
“This is mad, this is so much more than just an award. I want to just say first thank you to every single person who voted for us, it means so much,” he said.
“In a way, I have to say thank you to the people that complained, the people that did all of that abuse because you showed the truth. You showed exactly why this performance, this moment, was necessary.”
The celebrity dancer said that “so much needs to change” and urged people to “keep standing up for what’s right regardless of the colour of our skin.”
He said for him it was about “not representing the minority” and that “here right now, this represents the majority.”
Comedian Romesh Ranganathan was the first winner of the night, taking the Bafta for entertainment performance for his comedy series The Ranganation.
Inside No 9 was named best scripted comedy and the prize was collected by Reece Shearsmith, who joked: “We are in our sixth season, we have more episodes now than Countryfile, so we are going to keep going.”
Appearing virtually with the rest of the show’s creative team, Steve Pemberton quipped: “This is like the crappest episode of Gogglebox ever.”
Actress Rakie Ayola paid a moving tribute to murdered black teenager Anthony Walker and his mother as she won a Bafta for her role in a TV drama about the life he might have lived.
She was recognised for her performance as Gee Walker in Anthony, a one-off film written by Jimmy McGovern about the life her son might have lived had he not been murdered by two white men in an unprovoked racist attack in a Liverpool park in 2005 when he was just 18.
Collecting the best supporting actress Bafta, she said: “I would ask anyone, if you think for a second that you know anybody who thinks all they have is to take the life of another, do whatever you can to stop them.”
Malachi Kirby was named best supporting actor for his role in Sir Steve McQueen’s anthology series Small Axe, while Sex Education star Aimee Lou Wood won the gong for female performance in a comedy programme and This Country’s Charlie Cooper won the male comedy performance prize.
Sky Arts series Life & Rhymes won the entertainment programme gong, beating heavy hitters Strictly Come Dancing, Ant & Dec’s Saturday Night Takeaway and The Masked Singer.
Casualty was named best soap or continuing drama, with the cast accepting the award remotely, standing in front of the entrance to the hospital set.