Okay, I get that the riots were ugly, but the question of just who was responsible for the violence, and their actual connection to BLM is still pretty much undecided. Reports of just who instigated the riots are many and varied, and many, many fingers have been pointed at white supremacists. In this day of misinformation and media manipulation pretty careful about what one accepts as truth. Ms. Patel herself has stated that the "hooliganism" at the BLM protests came from a minority within the protesters, after coming under fire for criticizing the entire BLM movement for the violence and vandalism. A cursory look over Ms. Patel's recent history does tend to indicate a dramatic side to her public image.
The "List of Proscribed Terrorist Organizations" issued by the British Home office and last updated In July of 2020 makes no mention of BLM.
Home Office Terrorist List
The BLM movement is devoted to raising awareness of inequality and systemic racism, and has gained global recognition for drawing attention to these long standing issues. There is little real organization you could attribute to BLM, there's no one running the show. What we are watching is the frustration of centuries of mistreatment finally boiling over, something that was pretty much inevitable. The actions of a few, no matter what their political views, cannot be allowed to divert our gazed, even though there are many who would like to see the whole thing just go away for whatever reason.