The thing is, the politicians in Europe realise that migration from outside the EU is a major concern for the people and ultimately the numbers coming now are a fraction of what they were when people were falling off trains in Munich Hbf.
The UK, instead of working inside the EU towards a solution has opted to simply leave.
That's the UK's prerogative but the EU is actually capable of sorting this stuff out.
The UK had the ability to reduce half its inward migration (the non-EU component) to nil, had it so desired. It never really reduced it at all. The EU migrants can as we all know be sent home if they are not productive members of society. You are not allowed under EU FoM rules to simply rock up and claim benefits. The UK never bothered clamping down on this, indeed the UK (and Ireland and Sweden) were the only countries that threw open the doors when the new member states joined. Had the UK exercised its veto, like Germany and France, then the Polish community would never have established itself in such numbers in the first place (if you think Poles are a problem, which personally I do not).
The UK had 3 major tools at its disposal to limit migration from both non-EU and EU sources and did NOTHING and then went off in a huff muttering something about immigrants.