You usually start with 'people with a university degree are more likely to vote remain'. This is 2016. Anyone who can get 2 D grades at A level can get in to some university, albeit not often a quality university.
Let's take Kerry and James. Kerry is 22, and has just received her 2.2 in American Studies from the University of Wolverhampton. She voted remain because she wants to 'experience life' in Europe, and being in the EU will mean that she won't have to apply for a visa or pay roaming charges when she's on holiday before returning to work in a call centre.
James is also 22 and is the co-owner of a building contracting company that he started when he was 19. He voted leave because cheap migrant workers undercut British workers, and he is also worried about how the EU is becoming more authoritarian, and Turkey potentially joining it. He owns a home, has no debt and is called a racist by people online.
Still think a degree makes you more intelligent.
Lastly, the idea that Leave voters aren't just uneducated in general, but are also uneducated on the referendum. Because surely if they were educated, they'd vote remain, right? Right?.
Us working and even lower middle class people are fed up of being told what to do, how we're stupid and uneducated. Whilst you're sitting drinking coffee and eating artisan bread and reading the Guardian, we see nothing of benefit from the EU.