The Brits dithered for years, and then stood up to fight the Nazis. When they get through dithering, I'm sure they'll do what we should be doing now, which is send all of these folks back to their home countries, dynamite their mosques and go a little insular for a while. If the government doesn't do it, I am confident that the British themselves will take over the task.
I'm pretty pessimistic about that too. These aren't all people who just 'got off the boat'. These are 2nd and 3rd generation Brit/euro citizens that you're talkig about. in 42 it was easy to identify the enemy. It's gonna be a lot harder now, even if the brits could muster the will.