Class is a weird one. I agree that it isn't really relevant today,
I am as working class as they come - Dad worked hard all his life but we lived in a condemned slum when I was born. We moved to a council house, ate bread and dripping, wore hand me down clothes which were darned.
I suspect nurture might play a part now as to where we fit, and aspirations of course. My parents loved reading and we were read to and would read anything we could get our hands on. I lapped up learning as a result. Comprehensive school education (in it's infancy back then) and it was strict and I don't think I could have had better teachers. They introduced us to classical music, Latin, poetry, languages, the arts. I left with good A levels and went on to higher education, twice. Education might be the key?
I went on to become a decision maker, hold meetings and manage large teams of people, some of them better educated than me, and earn a good wage. My accent didn't change. I was also a single parent for much of my working life, so was never really affluent.
Flat vowel sounds put me in my place probably, but I have had a richer, more 'upper class; experience than many I suspect. No idea where I fit in but I appreciate my roots.