I'm not convinced it'll happen tbh.
51.89% vs 48.11% is far too close to be considered a strong mandate. (only 37.44% of the electorate actually voted to leave)
I envisage 2 possible courses:
1) General election in October, with 1 major party offering to repeal the referendum result. (16M votes will
easily win a UK general election)
or
2) Due to the weak mandate, the negotiations will be slow & cautious, and will result in a 2nd referendum on the precise terms of the separation. This period will cause enormous upheaval & cost, but will hopefully knock some sense into the electorate, allowing a reversal of the decision.
Whatever happens, the UK needs to reform its electoral system.
First past the post is terrible, and using referendums to reverse major political decisions without requiring an absolute majority is idiotic.
Of course the 1 recent attempt at electoral reform failed because.... *sigh* voter ignorance?
In a 52-48 referendum this would be unfinished business by a long way.
So it looks like Farage along with 2.6 Million people are already supporting a 2nd referendum:
https://petition.parliament.uk/petitions/131215