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I don't think the remain campaign was particularly effective (though the leave campaign also seemed pretty disorganized and amateurish at times), and I think Cameron was a little overconfident, but it's ridiculous to suggest that the remain side didn't really care about the result. It was obvious that Cameron's political career depended on getting a remain victory, so of course he worked hard for it.

The referendum was purely advisory, so it's up to the government to decide how they want to interpret the result. There is no "custom and practice" of requiring 2/3 or 75% supermajorities in the UK, and judicial review is pretty limited here anyway. The goal of the referendum was to deliver a blow to Ukip and the eurosceptic wing of the Conservative party - anything that made the referendum seem biased against them would have just made them more angry and self-righteous.