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In addition to that, British politics conveniently used Brussels as a scapegoat in order to cover up their own inability to deal with Britain's problems. It was easy: Politics blamed the EU for everything that was wrong in Britain and the Yellow Press actively supported it. After decades of propaganda bombardement, many Brits today actually believe the EU is something evil, a totalitarian system even that exists to destroy national identities and make all of Europe standardized and identical.
And that's not going to change. No matter how the separation between GB and the EU will be handled, somebody will always call "bad blood" between the two and blame every decision made by the EU on the need for "revenge" or "being extra hard to spread fear into the remaining countries". There is no way the EU can come out of this clusterfuck anything but a villain. At least to the British people. And really there is not much choice either. If the EU makes concessions, like for instance granting access to its market without also having to take part in the Schengen treaty, then it will be reduced to a total joke. There simply can't be any special treatment - especially since many people in continental Europe were already pretty pissed about the super special treatment that GB was getting so far.
I still can't really believe we're going to leave the E.U. The whole thing just seems surreal. I also think both the U.K. and the E.U. are being a little petty about it all. Leaving doesn't seem to be a good idea for either party. It's just energizing the far-right groups in Europe and has completely thrown Westminster, Holyrood and Senedd in to complete chaos.
So what are our options? As far as I know the British Government said it would follow the result of the referendum. If it suddenly changes its mind and ignores both the result and what it said it would do, well, that doesn't look too good on the politicians and democracy in general.
The next option would be have a second referendum, because the first one was "close" or "the result was stupid". Also doesn't bode well for the general state of modern democracy, since it suggests that if you don't like the result of a poll, you just have a 2nd, 3rd or even 4th poll until you are satisfied with the result.
So far so bad, but maybe we can blame it on lying politicians during the Brexit campaign? Well shit, politicians - especially the ones that don't have much or any power at all - probably lie all the time (because usually almost nobody listens to them and also they don't have much to lose). So you're at least partially responsible by blindly believing what someone else tells you. We live in the 21st century and there is something called "the Internet" with hundreds of opinions from all around the world at your fingertips. Some people *wanted* to believe the crap that was sold during the campaign. Or they were too lazy to check what the media in other countries thought about the whole idea (hint: it's always a good idea to check what others think of you - you don't necessarily have to follow any advice but it's good to have a rough idea about how you and your actions are perceived by others).
TL;DR: This whole mess is a total clusterfuck and I don't see an easy way out. The EU can't show any weakness and right now GB can't go back and pretend that nothing happened.
My personal opinion is that GB had a pretty sweet deal with the EU and threw it all away. And I freely admit that I'm worried for very selfish reasons: Switzerland is depending on the well being of the EU without having much of a say in the matter. I work for a company that sells to customers in Europe and GB. We depend on favorable exchange rates and the fact that people in other countries can afford our products (which are "premium" with "premium prices" to say the least). Friday last week the swiss national bank again had to keep the swiss franc from going up like a rocket. Keeping it down burns money, but keeps the export industry alive.
I think if you want to leave the EU, by all means feel free to do it, but do it in a way that doesn't take a whole country/continent with you. Just move somewhere else.