Democracy cannot succeed if people and politicians set up government policies along the idea of majority rule. Instead, you have to go back to the guts of it all: happiness for the people.
With a concept like Brexit, where roughly half the population of the UK want to leave the EU, and the other half do not, compromise is in order. Brexit shouldn't mean Brexit, and to run with that conclusion is to blindly follow a nascent and unrefined buzzword. Is Brexit going to hurt the UK? Then just maybe you need to REFINE the theme.
"Oh, but a majority voted for Brexit". Bullshit! They voted for all different things, and for all different reasons.
Brexit SHOULD mean fucking fixing the problem so that WAY MORE than 50% of the population is better off, and the few others should at least not be harmed.
That's what democracy is SUPPOSED to be about: compromise, make the imperfect world a little better, and repeat forever.
The US has the same problem. The gun lobby can't even begin to compromise on obvious ideas like "risky unstable nuts shouldn't be given guns". Politicians, who are real humans, actually support this idiotic position despite the realities of a complex world and a well-oiled legal system. Instead of these politicians being fucking idiots, why don't they work to fix the fucking problem in a way that is achievable and makes reasonable sense? Oh no, that's too hard? You're unwilling to compromise? You're a politician, you idiot! It is what you signed up for!