Perhaps it is now, but it was not always the case. At the dawn of age of reason you would have certainly needed to be independently wealthy (upper class) in order to pursue purely intellectual activities.
For a time, anti-intellectualism was perhaps not as prevalent within the working class. Education was seen as a way to better ones self, people tended allotment gardens and took part in sports and cultural activities like workplace brass bands. Maybe they succeeded and their descendants are now middle class. The reality though, is largely defeat as was alluded to in this thread:
https://news.ycombinator.com/item?id=16272553
"Chavs: The Demonization of the Working Class"
"There’s been class warfare for the last 20 years, and my class has won"