The BGT champions appeared on last year's show with a routine about the Black Lives Matter movement.
The performance by the 2009 winners of the show was met by acclaim - as well as criticism. Thousands of complaints were made to TV watchdog Ofcom about the performance, all of which the regulator rejected.
Diversity stars and brothers Ashley and Jordan Banjo accepted the award.
Ashley said: "This is mad. This is so much more than just an award. Thank you to every single person who voted for us. It means so much.
"Thank you to every person who stood by us and every phone call, text, comment, DM, you guys made a difference in what was a really dark time - being in a storm of what was 30,000 complaints, a torrent of racially charged abuse, stress - but that support made a difference."
He continued: "In a way I have to say thank to those that did complained, that did that abuse because you showed the truth. You showed exactly why this performance and moment was necessary.
"But this is what change looks like and I'm so proud to be standing here, so thankful.
"For me, this is not about representing a minority, this represents the majority. Let's keep having those difficult conversations, let's keep standing up for what's right regardless of the colour of our skin and we will achieve that equality."
Prior to tonight's awards, Ashley appeared on The Jonathan Ross Show and confessed he was taken aback to the reaction to the performance.
He said: “I mean, yeah.. very surprised, we thought it would ruffle a few feathers, but not be one of the most complained about moments of the decade.
"The reaction, even still to this day, the online reaction I get on a daily basis is shocking, actually. But I’d do it 100 times over.”
Ashley continued “I’m just massively proud of it. It was controversial, made a lot of people unhappy, but it also made a lot of people stand up and be proud. It made a lot of conversations happen that needed to happen. Only this week, the performance itself was Bafta nominated. Fingers crossed. To win it would be incredible.
"Just to be nominated itself for me is just incredible... That performance, it was life-changing, it was incredible.
"To potentially win a Bafta for something that was controversial when it shouldn’t have been, it will be something that stays with me for the rest of my life.”