OH MY GOD let's get several things straight about Brexit

[Ironing Man]

146. simply, Parliament.

one of the upsides of not having a written constitution is that the Law is whatever Parliament says it is.

so, in the UK referendums are not legally binding - only Parliament is binding. Parliament (the 640+ MP's) can decide to ignore this result if they wish, it would be politically difficult, but there won't be another election for 4 years, and a considerable proportion of those who voted 'leave' don't normally vote - so Parliament could take a veiw that not only will this be ancient history in 2020, but that a sizable number of those who'd be all bent out of shape by their decision won't actually get around to voting them out in revenge. the referendum had a turn out of 72%, the general elections of the last 20-odd years have seen turn outs of around 62-65%.

alternatively, the government could ask parliament to pass another referendum bill on Monday morning - if a majority say yes, then we have another referendum.

another alternative is that we have a general election - Parliament trumps all before it, and one parliament can't legally bind the hands of a successor parliament - so if a majority of the MP's elected at that general election stand on a platform of disregarding the result of the election, (or some fudge which means the same thing..) there is no legal impediment to that Parliament halting/attempting to halt our exit from the EU.