Now, what do you do with that? Britain could have required some level of majority before making that change (60-40? 67-33? 75-25?), but they didn't. On the other hand, they could have made it a binding referendum, and if I understand correctly, they didn't do that, either.
But one of the big reasons people wanted to leave "the unpopular and undemocratic European Union" (as wjnc said), was that when people voted "the wrong way" (as determined by Brussels), that vote got ignored. If this vote gets ignored/sidelined/not implemented somehow, for the 52%, that's going to be pouring gasoline on a fire.
Even if most of the voters give their best effort to think this through, for a lot of them that wasn't much, other than what UKIP barfed into the air and into their minds. Now a lot of them are having second thoughts.