We had BLM protests here in Britain too, but George Floyd isn't the main reason we've grown to distrust cops.
Two years ago, a serving Metropolitan police officer 'arrested' a young woman who was walking home from her friend's house on the basis of her breaching COVID lockdown guidelines. He then raped and murdered her. The Metropolitan Police then proceeded to brutally crack down upon a peaceful vigil held to mourn her.
Wayne Couzens is thankfully serving life without parole for his sickening crime, and the ladies who were manhandled, tackled down and detained during the vigil have been compensated by the courts. This whole scandal because the catalyst that led to Cressida Dick resigning as the Met Police Commissioner (long overdue), and investigations that found institutionalized racism and misogyny in the Met.
Another example is the 'Kill the Bill' protests, which were protests held against the Police, Crime, Sentencing and Courts Bill which was going through Parliament, which essentially wanted to give the police greater powers to suppress peaceful protests and dish out ten year prison sentences for causing a public nuisance. This came off the back of environmental groups blocking roads to protest the government's inaction on climate change.
Protests to oppose the bill led to a riot in Bristol where a police station was vandalized, and a later protest which was cracked down upon with violence. I remember seeing a clip on Twitter of a police officer bashing a woman in the face with his riot shield.