It's absolute rubbish to say the working class shun education by definition. My father was a milkman. He left school at 14 and started to earn his living right away. This was in the 1920s during the depression and he had to help support his younger siblings. His own father left school at ten years old and worked on the fishing boats out of Dunwich until he went off to war in 1918. Both my father and grandfather, despite their short time in school, were well-read, articulate men who played chess at championship level.
My father urged myself and my older brother and sister to make the most of our opportunities and work hard at school. Education was valued in our home and in the home of my friends. Most of our fathers had skilled or semi-skilled jobs rather than professions, and most of our mothers stayed at home.
I did not become a fully-qualified teacher until I was forty years old and despite having the benefit of a longer education than my parents, I could not go to university until I was in my thirties. This is because both of my parents died during my last two years at primary school and I could not expect the various carers who raised me following this to support me through university.
I don't think you have a full understanding of the historical meaning of working-class. Certainly, there seems to be a layer of society who do not value education, and I suppose a case can be made for them being regarded as working class but not in the true sense of the term. They are in no way part of the proud class of men and women who build this country and created its wealth and fought for the benefits and opportunities enjoyed today. I include in that great fight many worthy middle and upper-class folks too of course.