The Brexit referendum itself was a textbook example of direct democracy; however, direct democracy is not a part of normal British governance, which relies on having a strong majority party in Parliament to make decisions. The referendum could not be binding, because that would contradict the established tradition of Parliamentary sovereignty. But Cameron let it go forward anyway in the mistaken belief it would fail, because he was too much of a coward to stand up to the Eurosceptic branch of his own party and thought he would gain political advantage from it.

Everything that happened after the referendum is purely a function of having a divided ruling party, resulting in a relatively weak government, combined with self-interest and political cowardice.

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