The problem with the blame game is that the main culprit isn't on the table. Social cohesion and the lack of it is a problem in every Western European member state. Lack of support for the EU is a problem in the whole of Western Europe, not just in the UK. In every Western member state the working class is on the wrong end of the deal.
The EU as an institution has failed miserably. It really wasn't that hard, Europe was already there, a continent full of stable social democracies with people who want to and know how to trade with eachother, who want to travel, move and live in different countries, who want eachothers products and want to compete with eachother in a friendly spirit and who respect and enjoy eachothers differences and cultures.
Basically all they had to do was to organize a transparant and democratically controlled bureaucracy to remove the barriers that stood in the way of Europeans beeing Europeans and act European. The economic activity that is freed up by removing the barriers will make everybody more wealthy. Instead, they used the building process of the institution to take away the power from democracies and give it to multinational companies and take wealth from the working classes and shift it to the haves and the haute finance. And while doing so, it creates crisis it can't solve and worsens crisis it didn't create.
The UK really isn't that unique, it's not like that if those crazy waveruling people are out it's just business as usual with the EU. There will be more referenda, civil unrest, protests, strikes, road blocks, riots, boycots etc. The best thing that could happen right now is that this Brexit gives momentum to the broad European sense that the EU really needs to change fundamentally and that the national politicians and het EU ones go back to the drawing table and come up with a EU that has solid public support. And I don't mean 52% or something, there is no good reason why a EU that works for the people wouldn't have the support of at least 70% of each of the populations. Also there's no good reason why this can't be decided within two years. Like all other member states, Scotland and Northern Ireland, the UK deserves a better EU.