I have to disagree with you about Brexit. Again, this only comes from talking with and listening to people as an activist and occasional campaigner, so let's enter that caveat from the start. As far as I could see, the tertiary-educated middle-classes - my contemporaries in age and younger -were solidly pro-EU. Those of my parents' generation, who grew up during WW2 and the 1950s, were equally solidly pro-Brexit. However, working-class people of every generation were very pro-Brexit, and had been since a few years after the UK entered the Common Market. From their viewpoint it had done nothing for them except put prices up and allow foreign governments to dictate to us. They distrust the Germans and despise the French. They hate "all those bloody silly regulations that mean you have to fill in a pile of forms just to do your job", and so on. I'm not saying those opinions were in any way valid or rational, just reporting what I've heard. For myself, as a Socialist I was aware that far too much EU policy was pro-corporation and diskliked the way that 'free movement of labour' was used to create a mass of itinerant unskilled workers who were used to push down wages and conditions in any EU countries who tried to implement pro-worker policies.
In the matter of education, I was a scholarship boy at a (very) minor public school. There were two things my school had that my contemporaries in State schools didn't have. One was the active involvement of parents who took an eager interest in maintaining high academic standards and discipline. working with the staff rather than against them. The other was the holistic ethos that said the school was about creating well-rounded, well-adjusted citizens, not just getting them through exams. I agree that the major public schools are bastions of privilege and require greater regulation, more diversity snd so forth. But at the same time, State schools should be encouraged to partake of the ethos I mentioned. The obsession with tests, exam results and league tables has to be expunged, and efforts must be made to convince parents to be more involved. Too many just dump the kids at schol in the morning, pick them up in the afternoon and often don't even ask about their day, much less check up on homework! Somebody needs to counter the pernicious influence of employers, who want work-ready, compliant drones rather than educated people!