Looking at the overall vote I think it's clear that Education was much less of a factor than age. The oldest group of voters, particularly those of 65+ voted hugely in favour of Leave. I think a large part of the reason for that was the rose tinted glasses of nostalgia. People like my dad waxed lyrical about an England that so far as I can tell never really existed outside a film or book. Farage played that card particularly adroitly with his tweed jackets, woollen ties and lots of shots of him in "ye olde pub" drinking brown beer. He was so blatant about it that I half expected him to pull on some driving gloves and jump into an Austin Seven, stopping off to watch some cricket on the village green before heading back to his thatched cottage in the cotswolds. I wouldn't have been surprised to see Noel Coward and Jack Hawkins pop up somewhere with a voice over by Laurence Olivier and extra narration by John Mills.
Unfortunately too many of the older generation believed the hogwash and think somehow that the Empire will rise again once we're "free" of those swarthy Johnny Foreigners who've come here to steal our jobs and corrupt our womenfolk. The fact they won't have to live with the long term consequences of the utter disaster that Brexit will be only makes the whole thing even more tragic imo.