According to The Guardian , the referendum is not legally binding, and the final decision lies with Parliament.
politics.stackexchange.com/users/8467/Eduardo
The ultimate authority lies with parliament, but…..
The UK Parliament has a history of avoiding outcomes like the French Revolution.
So it will need a very good reason for the UK not to leave, this would have to be something that was not expected at the time of the referendum.
Most MP would have to believe that ignoring the public vote was more important then every getting elected again.
politics.stackexchange.com/users/4800/Ian Ringrose
Constitutionally speaking, it is impossible for any prior decision to bind the British Parliament in a way that prevents them from making a different decision at some later point.
In this case, the possibilities are interesting.
Cameron has stated that he feels a different leader should take control of the process rather than himself.
There will now be a leadership contest in the Conservative party, and the results have the potential to be interesting.
One plausible scenario is that some substantial portion of the Conservative party is unwilling to accept a new leader, resulting in the leader of the party being unable to present himself as having a commanding majority in the House of Commons (i.e. he/she would not be able to become Prime Minister), a situation which would lead to a new general election.
Some existing Conservative MPs might defect to other parties or form a new party.
Parties other than the Conservative party might not feel obliged to honour the result of the referendum, so if say a Labour/Liberal coalition ended up in charge of the Commons in a new Parliament (which is certainly a possibility if Conservative defectors split the vote in key constituencies), Article 50 might never be invoked.
All of this is, of course, highly speculative, even downright unlikely , but it is possible .
(As a supporter for electoral reform, I will point out that this scenario would be even more unlikely had the UK switched from first-past-the-post to AV after the last referendum.
But that's probably beside the point.)
politics.stackexchange.com/users/8576/Jules
It is not binding.
However, it's a democratic voting
and I don't think a democratic parliament will disregard a democratically achieved decision.
politics.stackexchange.com/users/8642/BobbyPi
While the referendum is not legally binding, it is in practice.
David Cameron had said he'll invoke Article 50 immediately in case of a leave vote.
While he has now said that he'll leave doing that on his successor, it's politically inconceivable that Brexit won't become a reality.
In fact, the Brexit train has already left Brussels, UK's EU commissioner Lord Hill is resigning
and it's unlikely that Britain will nominate someone else to take his place.
politics.stackexchange.com/users/4235/Count Iblis
Now that the implications of the leave vote are becoming clear there are a number of issues that could prevent the UK from actually leaving the EU.
For example, many leave supporters seem surprised that the currency and market reactions were so severe despite clear (having dismissed warnings from the remain campaign and from experts as scare mongering).
Strictly speaking the referendum is advisory but it is unlikely that parliament would want to block the act of leaving.
However, things are not so simple.
The political chaos caused by the vote is likely to lead to a general election and, depending on what happens in that, the new parliament will have a different mandate and might feel it has the authority to ignore the referendum.
Moreover, it is already apparent that the implications of leaving were not clearly understood by the electorate or by the leave campaign (who never had much of a coherent view of what the terms of EU departure would actually mean).
Some leave campaigners want a radical departure from the single market and tight control on immigration; others want a Norway-style deal that leaves the UK in the single market but this is impossible if free movement is abrogated.
Until government has negotiated a specific deal it is impossible to judge whether people would be happy with the terms.
While there was a narrow majority for a vague commitment to leave the EU (where the voters could believe whatever panglossian, incompatible terms they wanted to), there might be nothing close to a majority when the specific terms are clear.
This implies either that parliament could say staying is better than the specific deal negotiated or they could argue that a second referendum is required to allow the people to vote on the specific departure terms.
So, even if parliament treats the result as binding, it doesn't mean it can make the actual decision to leave the EU without some further work.
The most government can do is to negotiate a deal and, if the implications of the specific deal are unbearable, they would have to seek a further mandate to actually sign it.
PS
As I was writing this Nicola Sturgeon claimed that the Scottish government might actually be able to veto any decision to leave.
So the legal authority of the UK parliament might not even be enough to trigger the act of leaving.
It looks as though nobody had fully though through the legal implications of Brexit.
politics.stackexchange.com/users/8658/matt_black
The BBC has projected that a majority voted for the UK to leave the EU.To what extent is the referendum binding?
Must the UK leave the EU?
politics.stackexchange.com
<united-kingdom><european-union><brexit><referendum>
politics.stackexchange.com/questions/11344
politics.stackexchange.com/users/8542/Colin
According to  The Guardian, the referendum is not legally binding, and the final decision lies with Parliament. While the referendum is not legally binding, it is in practice. Now that the implications of the leave vote are becoming clear there are a number of issues that could prevent the UK from actually leaving the EU. The referendum is not legally binding.
The referendum is not legally binding.