I think this result is consequence of a common frustration with politics, a frustration exacerbated by a comparative reduction in the economic security of the working class and the less educated.
The advantages to "reclaiming our sovereignty" are hollow, especially compared to what will soon be lost. Most arguments for leaving were outright deceitful. We had a privileged position in the world's largest trading bloc (full membership with numerous valuable opt-outs), and we benefited greatly from it (even from the EU migrants). But we just voluntarily gave up our greatest trade advantage... to start our trade policy from scratch.
And yet, the impression I get is many Leave voters don't feel they'll lost anything except movement rights they'll never use. Rather, they've gained a moral victory by asserting a kind of power of the people. They had an opportunity to do something, and they took it.
I think this all comes down to systematic problems in the UK. Rejecting a scapegoated EU maybe let people feel like they were accomplishing something, but it was absolutely the wrong establishment to target. I cannot imagine a future that will validate this decision. This will be bad not just for the state, but all its people.
I will be surprised if the UK somehow manages to address its societal and political failures better outside the EU than within it. Maybe now it'll be forced to, which I admit would be one good result. But at the moment I'm a bit overwhelmed with frustration that Cameron's short-sighted political maneuverings (coupled with a plethora of absurdly misleading Leave propaganda) have taken us out of the EU and may lead to the break up of the UK.