Of course there are some very educated Brexiters. But polls don't reflect individuals, they give a snapshot of the big picture.
The source for this was a YouGov poll from March 2016
yougov.co.uk/news/2016/03/24/eu-referendum-provincial-england-versus-london-and/
"Leave" more than 10 points ahead among:
Age 50-59, age 60+, Conservative/UKIP supporters, Telegraph/Sun/Mail/Express readers, Highest qualification GCSE or lower, C2-DE social class
"Remain" more than 10 points ahead among:
Age 18-29, age 30-39, Guardian/Time readers, Green/LibDem/SNP/Labour supporters, University graduates, Highest qualification A Levels or equivalent, ABC1 social class