There have been protests inspired by or related to Floyd's death, and the issues it raises, worldwide, Retrocop. I'm not sure why you've missed it, although to be sure maybe in the UK most of the news has been on home events.
But there's nothing uniquely British/Anglophone about the protest movement. We aren't even alone in reconsidering who deserves a statue -- Belgians have decided that Leopold II statues are probably in bad taste, for example.