I wonder if a snap election could be called before article 50 is invoked? One of the major parties could campaign on "Remain" and if they won, they'd have a democratic mandate to ignore the referendum.
The best chance the UK has to reverse the result of the referendum is Nicola Sturgeon being able to do what she suggested today, blocking the process of the triggering of article 50. If she really has the power to do that, then there's hope still. Otherwise, the UK is screwed.
Tbh I feel awful for Lizzie and Charles, who might end up being constitutional arbiters in the process of disgregation of a kingdom their family kept together for hundreds of years. They probably didn't expect to have to deal with this shit at their age.