Morning all, a few thoughts.
We have no tradition of regular referenda in the uk and there is no defining law that makes them binding or not. The lack of a written constitution allows parliament to make it up as it goes along, often this works, sometimes it does not. Such precedence as does exist shows that the government implements the choice of the voters.
However in the run up to the vote, the government committed to implement the result 'whatever it might be' and stated clearly that 'out means out', of the single market, customs union et al. I think the British people had the right to take the government at it's word.
The political machinations within the Tory party that MrT were important in that they contributed heavily to the decision to have the referendum, Cameron thought he could close down the leavers within the party and, expecting a remain vote, stifle anti EU feeling among some of the population. He got that all wrong, bottled it and ran.