Realistically, how? There are several million muslims alone in the UK, many of them second or third generation and no longer citizens of their countries of origin. What country will take them? Are we going to charter hundreds of thousands of deportation flights, or load them onto barges, or march them across the continent on foot?
This is going to end in pogroms if the government don't get on board, or sending people to camps if they do. It's unfortunate but I can't see a future where neither of those things happen, the problem has been allowed to get too bad.
It's not that hard at all. Populations get displaced every single day and we don't care.
As a start, you declare the UK to be the homeland for the European British tribe. Those that do not belong, can be tolerated as long as they are happy to live as guests, with fewer rights and privileges than the natives.
All discrimination laws are abolished. All affirmative action, abolished.
This will slowly push the non-natives into ghettos where life will become more and more unfun.
The government should also incentivize people to either leave, or assimilate. Assimilation means an almost complete renouncement of your culture, religion etc.
You want so much to stay in England? You will learn the language, we will test you for that. You will abandon Buddhism, Islam or Judaism. You have no rights to organize based on anything that's not native to the UK. You cannot make the Polish or Romanian party.
Refusal to assimilate will result in loss of citizenship and eventual deportation. Diplomatic deal should be worked out. Other countries are poor enough to accept financial deals.
Also, this is not about just Muslims, but blacks from parts of the empire, Indians, Bangladeshis, Chinese, anyone that's not British.
No need to rush, just go slowly, step by step.
could lead to radicalization
Cool!