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Given that the referendum is only advisory, a winner of a general election who had specifically campaigned on a platform of staying in would be well within their rights to ignore it.
And any government after that would have to think about putting it to a referendum again, as the legitimacy of this one would have run its course. Hence to an extent the number crunching that I'm trying to do to see how long this can be counted as legitimate for...
MrDrem-
They can't ignore it, they would have to reject it as demonstrative of a need for change in the country that doesn't necessitate departure from the EU. Once the Tories have managed to appoint a new Grand Wizard and Labour has resolved it's internecine shit-heeling then I suspect that there's going to be loads of shiny suited campaigning death squads going out to the proley sink estates to find out what the typical disaffected Leavewanker actually want out of government. They'll then beat a hasty retreat back to Whitehall to make up some shit while banging their heads against desks in an attempt to shake the pony fantasies of the provincial knuckledraggers.
You make a good point about the diminishing legitimacy of the current referendum though. Mind you don't rely on the fickle teenage vote as rock solid Remain.
The_Seldom_Killer
Whoever gets in could say "we shall leave the article 50 notice to the winner of the general election", breathing a sigh of relief that they have (potentially) a stay of execution, and then if the other team gets in (although vide the current debacle of the PLP, this may be unlikely) they could state that it's against their principles. Dunno how that plays into the "majority of the people have voted" aspect, but if you campaigned on remain that would add legitimacy.