As an aside, for me this is a sterling example of the dangers of "direct democracy", that many see as the solution of all evils that plague the political process.
The majority of UK lawmakers (democratically elected by the same people that voted the referendum) were in favor of staying in the Union: even a large number with conservative and traditionalist background (including the PM).
Yet the future of the UK (and EU) was decided by people (on both sides) that cannot possibly have an idea of what the implications of this decision will be, and that can be easily swayed my media and influenced by emotions.
Representative democracy has its faults and inefficiencies, but if the alternative is to have gut-reaction votes and petty nationalism decide the future of a country, count me out.