I think you overestimate the amount of migration from the EU into the UK - t was always overshadowed here by non EU migration.Most EU countries faced with the mass uncontrolled immigration that the UK has experienced would have reacted the same if not with more negativity. The UK is not, and has never been anti Europe. It just cannot see why it has to accept whatever is thrown at it from Brussels.
To be a sovereign nation which controls its own borders and immigration is simply a right enjoyed by most nations in the world. The EU is the experiment that has gone off track to suit the Eurocrats on the gravy train. They will ruin what was once a good idea with a free trade area. The discord between EU member countries continues to increase, nothing to do with Brexit.
I also think you overestimate the concern most EU countries have about migration - they just do not seem as bothered. That could be because for hundreds of years moving on the continent was easier than to an island.
I do agree that the UK is not anti-Europe - and more to the point mostly also not anti-EU. I do agree the UK though especially disliked the Commission and its seemingly undemocratic, dictatorial and bureaucratic nature.
The EU comes over as very arrogant and the UK has felt that the German-French accord has given us less influence than we might have liked.
Whatever the right and wrongs of those arguments once the UK voted to decide its own future the EU - like remainers had no choice but to accept it.