Democracy is not some sort of absolute good. The whole point of representative democracy is that even the will of the people has to be tempered. Constitutionally, in the UK, Parliamentary supremacy is the very core of the governing system. In Britain, as with the other Westminster countries, the people choose the Parliament, and the Parliament chooses the Government, but it is Parliament from which all fundamental lawmaking flows. The MPs have a higher obligation to the national interest than even to the voters, and if the voters don’t like the laws and policies Parliament enacts, then they have a General Election to voice their displeasure.
Leaving the EU is a monumentally catastrophic decision that will harm Britain’s economy, threaten it’s internal unity, and even the social cohesion within England itself. The entire referendum was nothing more than a stunt by Cameron to try to quell the MPs that John Major once referred to as “the Bstrds”, a bloc of Eurosceptics in the long tradition of anti-Continental sentiment.
If the Conservative Party, the oldest democratic political party in the world, has ever stood for anything, it is continuity and constitutional supremacy, and Brexit undermines all these things. From a geopolitical point of view, it abandons a policy that has been at the core of British statecraft for five centuries, that no single power should ever hold dominion over Europe. By leaving the EU, Britain essentially hands Europe over to Germany and junior partner France, abandoning its critical position as the economic and political counterweight to the German behemoth.
For historical context, the Athenians democratically voted to go to war with Sparta. By the end of the Peloponnesian War, Athens was subjugated and occupied, and its position as the pre-eminent Mediterranean power was over. So please spare me this notion that democracy in and of itself is a panacea. Democracy is more than a vote. The Westminster system’s delicate balancing of powers is one way in which democracy is balanced against the other necessities of government. The Framers of the US Constitution knew it, and were as skeptical of voters as they were of any other aspect of government, and by creating non-elected and indirectly-elected institutions, sought to check the popular will just as much as any other part of the political system.
And finally, quite simply, the referendum was non-binding. The Leave majority is a political problem, but not in and of itself a constitutional issue. Parliament remains supreme, just as it has since James II tossed his Royal Seal in the Thames and fled to the Continent in 1688.