I mean, I don't think a second referendum resolves the fundamental issue that having a referendum at all was incredibly stupid.
The entire point of representative democracy, which you arguably invented, was to ensure that there's still a filter between the mob and the world. That's what professional politicians are for, to take a set of generally unreasonable and contradictory desires and identify actually feasible plans and goals that will have mainstream support as opposed to 51% support.
It shouldn't be lost on anybody after the events of the last few days that if you removed the politicians who were pretending to support Leave but really just wanted more negotiating with the EU, the total number of MPs that really genuinely wanted to leave is probably around one.* Because leaving the EU is a stupid and terrible idea! But both saying "well the voters were uneducated" and saying "well even if it's wrong they voted for it" are not good responses to the issue. The issue is that it's unreasonable to expect the average British person to understand all the details of the question of EU membership enough to make a reasonable decision. The average British person, unlike the average MP, has a real job to do. They can't spend their whole day studying up.
Fundamentally the issue you're now grappling with is that setting this question to the general public at all was incredibly dumb. Literally the reason you have Parliament at all is to ensure shit like that doesn't happen.*
* And his name is Jeremy Corbyn.
** I mean, also to ensure that the Queen doesn't take unreasonable advantage of the royal forests, I guess, but controlling the mob is like job two at the very least.