Before being ordained in my mid-thirties I was a lorry driver and we lived on an East Midlands council estate. I left school just after turning sixteen and did not go on to further education. Even so I know I am an intelligent person and my wife is also (she manages a whole school in a university even though she has never been to university in her life). And here's the thing. We are not in any way unique. Working people are as equally divided between the clever and the not so clever as all classes of people. They are just as capable of working out who is lying to them as the academic staff of Oxford University. In fact, well educated liberals I know tend to follow the party line more unquestioningly than cynical working people ever do. Immigration was the crux of the referendum for them but not because of what anyone told them. It was because of their own experience. I agree entirely that the immigration issue was hijacked by racists for their own ends but they would have only influenced the very small minority of people (from all walks of life) who already buy into their extremist views. The vast majority of working people can spot a racist lie as easily as they can spot a Tory lie or a Blairite lie - which is very easily indeed.
Another accusation that the liberal middle class is levelling against working class people who voted Leave is that they "obviously" did not understand the economics because if they did they would not have voted to leave and risk economic chaos. But perhaps people looked at the predictions, fully understood them, accepted their accuracy and then decided that they were pig sick enough of being peasants in the fields of the rich, who rig the economy for only their own enrichment, that they were damn well going to vote Leave whatever. When you are very near to the bottom there is not far to fall and the black economy that serves the poor will always be there, EU or no EU.