Fair enough, let me clarify...I can only go on what you've actually written here, and it seemed to be that you thought Muslim immigration was a problem in itself.
In the US, a candidate for immigration can be denied entry if they want to undermine the constitution. I don't know if the UK has a similar rule, but they probably do.
So you ask all candidates if they support theocracy. If they say yes, they are denied. If they say no, but are later found to support theocracy, they can be deported for lying.
In other words, deny Islamists.