Nothing to do today so thought I'd look for the possible basis of the cartoons. I don't see a lie in the cartoonist interpretation.
Cartoon #1 seems accurate by stating MOSTLY Peaceful
Indeed according to Pew surveys the BLM protests became more peaceful over time. Between May 25 and June 4, 2020, 89% of protest demonstrations were non-violent while later between June and September 2020 more than 96% of BLM associated protests were non-violent [16].
Violence Against Black Lives Matter Protestors: a Review.
Cartoon #2 seems to reflect what is in this article.
The demonstrations are significant, however, in that they showcase the arrival in British public life of a new political force: namely, a mass, Islamist-led street presence that seeks to enforce its will on the public space and intimidate its opponents.
The U.K. Has an Islamist Problem
Cartoon #3 Info in this article seems to me it could be the basis.
UK PM To Meet Cops Over Stabbing Attack As Protesters Chant 'Save Our Kids'
More than 50 police officers were injured in violent clashes in the English town of Southport (AFP)
London: British Prime Minister Keir Starmer will meet senior police leaders on Thursday, his office said, between after a second night of clashes between protesters and police prompted by the deaths of three young girls in a frenzied knife attack at a dance class.
There were angry scenes in London on Wednesday evening as thousands of anti-immigration protesters gathered near Starmer's Downing Street office and residence chanting "save our kids" and "we want our country back".
UK PM To Meet Cops Over Stabbing Attack As Protesters Chant "Save Our Kids"