The great thing is that now that the UK has voted out, several other countries are going to follow.
"Liking or not liking" the EU is not the same as "in or out". So it is not going to happen.
Oh, Brexit would make a splash. But.
First. When UK economy would stagnate for few years - and NHS would see even less funding - even nationalists would come to their senses. First-world nationalists tend to lose support quickly, when people's living sandard is on the line.
Second. UK is unique in that it is living in a virtual media bubble. You have a completely perverted image of the EU, created and nourished by the media over the past 15 years. I know it, because 15+ years ago I was reading lots and lots of UK press. And the reporting was on completely different level. I have seen it changing from small stupid lies and half-jokes 15 years ago. To stupid unfustified accusations 10 years ago. To blatant lies and red herring - on front pages! - 5 years ago.
Some saner UK reporters are depicting that it is as if the people started believing their own lies.
Even here on the thread, most US readers know political system of the EU better than the most UK readers. And that's the f*cking Slashdot, where more or less exclusively only highly educated people are gathering. Let it sink for a moment: UK, being part of EU, knows less about EU, compared to the US who is related to EU only remotely.