I'm taking the liberty of lifting this from another thread I posted on earlier to explain at least in part, why it would appear that 'educated' people voted to remain and 'uneducated' people voted to leave.
The quality of a degree has for a long time now been debated. Other than the core professional degrees, many are in fact training by another name. Or indoctrination.
I replied:
This is true. I know plenty of(mostly young) people who have degrees but are by no means of superior intelligence to many older people who do not. Neither do I consider them to be better educated, more well read or more politically aware than most people without degrees.*
I think the 'educated people mostly voted Remain' and 'uneducated people mostly voted Leave' argument is rather simplistic and can be explained in part by the fact that young people voted Remain and ^older people voted Leave. In the last 20 years there has been the most enormous shift in the number of people going to university so if you look at the number of degree holders among the over 50's and compare it to the number in the under 30's you will get your answer.
I think it's a bit of a red herring and says very little about the intelligence of many voters.
That said, I don't doubt that plenty of working class, poorly educated, possibly quite thick, impoverished and disenfranchised people who blame immigration (and especially recent high levels of immigration) for everything and can't see past 'brown people get all the council houses' voted Leave.
But it is overly simplistic and patronising to simply state that uneducated people voted to leave and educated people voted to remain.