You're assuming those people are representative of the BLM campaign and acting on the direction of the campaign when there is no evidence they are.
In times of high public emotion (such as after the shooting of an individual by Police), you will always find some people getting involved in a protest who are just up for a public fight and really aren't that concerned about the issues.
They want a fight and it's particularly exciting when it's a fight with the Police and you come from a community who have historically been treated badly by the Police. People wanting to beat up white people just because they're white are not representative of the BLM movement.
I have experienced several protests and movements in my city in the UK which began with good intentions by people peacefully protesting with genuine understanding of the issues which were taken over by violent individuals seeking the thrill of a riot or a ruck with the Police.
I'm not in London but my city (among others) had riots after the Mark Duggan shooting. The majority of the people destroying public property, being abusive and violent to the Police and looting shops really didn't give a shit about Mark Duggan - it was just an opportunity to exhibit antisocial and violent behaviour with other like minded people. I had contact with many of these people after the event in my professional role and was told by many that they didn't really know why it was happening but saw a heavy Police presence and people 'kicking off" so joined in.
Possibly inflammatory protests always attract a number of people who are just looking for a scrap. You can't dismiss an entire social movement with good grounds to question government policy and the criminal justice system because some idiots have been idiots.
But it's always used by non - critical thinkers to ignore the real issues and blame the original protest movement. Happened with the Brixton riots (and others) in the 80s,.The Rodney King riots, Katrina looting etc and many, many more - oh but look - all these people from ethnic minorities are just violent and thieves and racist and they want to kill us!. See, this proves what this race is like! (implication being that the increased rates of arrest, conviction and killing of people of colour by the criminal justice system is necessary).
And SO many people including you fall for it.