The remain leaning newspapers wanted make a link that leavers are low educated, xenophobic morons on benefits.
I'm quite sure that if you took a decently sized random sample of people living in a country, where: cost of living, wealth, education, country of origin, age etc etc varied vastly, you could argue that it told you than northerners were thick and poor and southerners were rich and smart. Of course the smart person compares them against their peers. Unfortunately since nobody put their qualifications, income and age on the voting form, all the stats compared the demographic of areas voting leave vs the demographic of areas voting remain. The media agenda wanted to use this to imply that leavers were thick and remainers smart.
You cannot reliably conclude this.
I suspect you can count the number leave voting EU Law professionals living in London on one hand, just as you could the number of out of work cabbage pickers in Lincolnshire who'd vote remain.
Based on this poll we have 3 degree educated leavers and 1 degree educated remainer - pretty conclusive that leave voters are smarter than remain - Not