As John Kerry once said about something else, 'it's complicated'. Leaving aside your main premise, since frankly, the color of one's skin doesn't automatically make one a bomber, etc., but hate, envy, an ingrained sense of injustice fueled by a cult religion promoting murder certainly helps, Britain seems to have a segregation problem. And yes, they did allow in a great many from the Commonwealth -- as France let in millions from Algeria, gave them low paying jobs, segregated them in slums, and didn't allow them to become full fledged French citizens.
Britain's class system (aristocrats and everybody else), and the near worship of the monarchy on display 24/7 in the media are contributing factors. Think about Dodi Fayed's father, convinced the queen had his son and Princess Di killed because Di might have married his son and borne his child. This man is wealthy and powerful, yet he's paranoid. Or is he? The point is, Britain hasn't successfully assimilated her ethnic minorities. Worse, under pernicious PC'ism, she pandered to Muslim Islamofascists, allowing them to run amok. Other countries, including the US, France, and Germany begged her to put a stop to this, but she didn't. Well, feed the tiger, and when he really gets hungry, he'll eat you.
Britain suffers a huge guilt trip about its vanished empire, how they got it, what they did with it, etc.. They should get over that, concentrate on their great history and contributions to the world and teach that in the schools. Make every single Britain, no matter his/her color or ethnicity feel as if they belong, they're part of the fabric of the UK. (The US should do that, too.)
Apologies to MadIvan, but I've been trying to figure out what went wrong in Britain and how to fix it without mass deportation of several million Muslims or the tubes being bombed every other day. If my post came across as too harsh, again, I'm sorry. The US certainly has had her problems with segregation and injustice, and we still do. We'll have more attacks here, too.