It’s important to realize that Brexit is a bit more complicated than the rhetoric would have you believe. First it began with a combination of simple populism/nationalism/jingoism in the form of UKIP and at the same time a section of the political class in the Tory and Labour parties. For the Tories (at least the ones who became ERG members) it’s pure self-interest. They are filthy rich and like many filthy rich businessmen they think they’d thrive in a more lenient regulatory environment. They can create that environment for themselves if the EU is out of the picture and they keep power. Labour is more Remain, but Corbin and his fellow hardliners want a Brexit because they want the UK to be Socialist/Marxist. They know that’s just not going to happen in the context of the EU.
So you had Farrah’s and others playing the usual “Hey struggling masses, all of your problems are those immigrant’s fault” game. Over time the political success of UKIP and internal strife within the Tories led David “The Chinless Pudding” Cameron to promise that he would hold a referendum on the issue of re-elected. At the time he assumed that he would win by the same narrow margin he had previously and once again would enter into a “power-sharing” deal with the Liberal Democrats. He could then blame the LibDems for blocking the referendum, defuse the Tory civil war, and shut Farage up for another election cycle.
Then he won, decisively, and the LibDems tanked. So Cameron had no excuse to not have the referendum. He assumed that people who had been openly pro-remain such as Boris Johnson would put aside their personal ambitions and support Remain, but of course that didn’t happen. So what you had was a group of highly motivated people such as Boris who used this as a means to get power, people like Farrage being populist demagogues, and the ERG playing ideologue while just looking to get even richer. Cameron quit and literally walked away humming a little tune, and the Tories went to war with themselves. In the end everyone “died” and out of the ashes rose the silent one, Theresa May, who had switched from staunch pro-Remain to equally staunch Brexiteer mode overnight.
The rest is history. In a sense at the highest levels where Brexit isn’t about gaining short-term power and settling grudges, it’s about the long-term goal of being able to capture UK regulatory bodies. “People” like Jacob Rees-Mogg see how the business class can rob the state in the US, and they want a slice of that. The EU would prevent much of it, so they want out of the EU. The details of why individual people (who bothered to vote at all) voted to Leave is a lot less interesting and has less to do with Brexit than the political reality.