HM The Queen could provide an escape route from Brexit UPDATED

Ultimately Britain is a constitutional monarchy as well as a democracy. This provides a potential escape route from the Brexit disaster which would break up UK and EU.

It could justified by the fact that Leave won the vote with an extremely small margin

1. Reigning Monarch dissolves current government (whose sitting PM is about to resign anyway)and calls for a general election
2. New government after election refuses to invoke Article 50 kicking off the process
3. Brexit never happens (unlikely - see bottom)

CORRECTION

"The Queen previously wielded the power to dissolve Parliament and call a general election, but the Fixed-Term Parliaments Act put an end to that in 2011. Now a two-thirds vote in the commons is required to dissolve Parliament before a five-year fixed-term is up."

but

"While the overwhelming majority of the Queen's prerogative powers are devolved to her ministers, there is one exception that allows her to wield power herself. Only "in grave constitutional crisis," the Sovereign can "act contrary to or without Ministerial advice." With no precedent in modern times, it's not clear what would actually constitute this, but the possibility remains."

http://uk.businessinsider.com/weirdest-powers-queen-elizabeth-ii-british-sovereign-prerogative-swans-dolphins-2015-5

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The Monarch functions as a major force for national cohesion. Not only does this give her the right to intervene on this extremely divisive issue, she would probably be the only voice that the Leave campaign would respect.

It would also be one in the eye for the tabloid newspapers which have falsely claimed she backed Brexit, and which have been the bane of the lives of the Royal Family for some time.

"A vote for Brexit will not be determinative of whether the UK will leave the EU. That potential outcome comes down to the political decisions which then follow before the Article 50 notification. The policy of the government (if not of all of its ministers) is to remain in the EU. The UK government may thereby seek to put off the Article 50 notification, regardless of political pressure and conventional wisdom."
FT.com

There is an incredible theory that a Brexit won't actually happen even if the public votes for it
BusinessInsider.com

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UPDATE
After a nights sleep I can't see a way of avoiding Article 50. The way the vote was formulated, with a simple majority required rather than 60-70%, was a recipe for disaster and national division. Even if the vote had gone for Remain with this margin I think we could still have been looking at serious disaffection and trouble (but without the massive worldwide political and economic consequences).

I can see a case for having Article 50 implemented by a new government in a hugely changed situation. Not a new government formed by a treasonous political entity which has no mandate to govern whatsoever.

If you claim to stand for the United Kingdom but enact measures which you know will break up the United Kingdom (via Scottish independence) you are nothing but an English National Party in hiding.