At the risk of invoking British ire... They have had more EU integration of a certain kind than anyone else — actual large scale labour migration. The EU's extension eastwards was pushed not least by the UK, which saw it as a means of undercutting the trend towards deepening integration of the EU core member states. A large expansion would make that more difficult, and it has. It's just that when a large group of nations with rather lower living standards came in, a lot of individuals made individual decisions about using the free movement of people and labour, and since the UK speaks English, they disproportionally headed there.
And it matters because the UK is still heavily divided by class — the referendum revealed more of it that than might perhaps be entirely recognised? The UK has a wealthy London and south-east, which dominates the country, and large areas of the country done hard by. The UK also has a large low-wage sector with poor job security, where the working class compete with imigrants, and not just from the EU. (The irony is that the EU spends largely on the underprivileged bits of the UK — like Liverpool, where Thatcher's lost in 80's could talk about the need for a "managed decline" of the city, to crush the working class after riots, but where the EU has spent heavily on urban renewal instead.)
I'd say the EU's actual acitvities in the UK have been inoccuous or actually helpful. But the British perception of the EU is totally negative and has been for at least a generation. Even the media that are by British standards EU "friendly" pretty much just stick to not publising bogus claims about the nefarious EU. The reporting is next to 100% negative, or no reporting at all.
Frankly, as far as I can tell, this is now beginning to look increasingly like a revolutionary situation in the UK. It hasn't had that many.
The really serious ones was rather a long time ago. I'm now having run-ins with Brexiters who proudly explain that it's about more and deeper values than the economy, and that the EU just understands the price of everything but the value of nothing. The problem is that this is the complete inversion of what continental revolutionaries (French, German, Russian) have historically accused places like the UK, US, France even, of — of being crass, money-grubbing, old and decrepit, while their alternative (even if it's going to cost) is an inherently superior, more humane order of society (French "mission civilisatrice", "deutsche Kultur").
Right or wrong, the tenor of more British people than I would ever have imagined is sounding downright revolutionary. The Germans are confused — they're used to the British claims of level-headed pragmatism, against the "continentals" in the EU and their supposed high-falutin' idealism. Now there are British histrionics about an abstract form of "soverignity", which was supposedly under threat, but has now supposedly been saved... By comparison, it's "keine Experimente" Merkel's Germany that is increasingly looking like the balancing pragmatic power in Europe — whether it intended to or not. While the UK is off on some increasingly weird tangent.
