Do you think the class based system England has, played a role?
Weirdly..... I don't think so, not "Class" per se. There were some interesting trends if I recall.
The older generation were more likely to vote Leave. People with a higher standard of education were more likely to vote Remain.
Electoral wards with higher ethnic diversity tended to vote Remain.
Urban deprived areas were more likely to vote Leave than Inner City deprived areas.
I suppose you can say there was a "Posh/Poor" divide but it was more complex than that.