I think the nationalism vs globalism framing is correct, but somehow misleading. I love the cultures of countries, but am a globalist.
I don't like that capital is far more global and well-treated than labour is, but at least the EU made some strides in the direction of more movement for people.
However, while in principle the EU is great (my only problem is that it isn't globalist enough), the practicalities seem to have been co-opted by international capital.
For instance, law-making powers are still reserved to the Commissioners. Politicians who never have to run for elections again are not the right people to put in such a role, and yet, that's what happens.
The Council of Ministers are even worse. All the national governments get together, fight, make a decision that the EU then implements, then each national government goes home and blames the EU for it.
Meanwhile, things that would actually make life better for the people of the EU (roaming charges are a good example) are held up for years because they damage sets of national interests.
Don't even get me started on the Euro.
On the other hand, the EU means that western europe and some of the rest has been in relative peace for over sixty years now, and there is definitely more of a sense of common identity across the countries, which is brilliant. We've changed from young men dying in the muck to old men arguing over idiocies, and while that's not a perfect change, its still better than the alternatives.
But the forces of maximising profit by shifting work to lower-cost countries are the real causes of the hollowing-out of much of the UK outside London. This, along with perceived loss of identity, causes those people to lose faith in all of the internationalist movements which are backed by capital, and vote Leave.