I think it's probably more to do with education than anything else, with a huge amount of overlap with how you choose to express yourself (speech/possessions/activities you enjoy/home).
Education can be formal, or on the job. I don't think a degree is a defining feature of a middle-class person. I'd say self-education for its own sake doesn't count.
In my family we have a spread of classes, despite all being from the same stock. My dad is middle class: left school at 17, got himself a white-collar job, worked his way up, owns a house outright, holidays in a gite in France, reads the Independent etc.
His sister, my aunt, married a soldier at 18, had children young, manages a care home, reads misery lit, has octagonal black crockery, technicolour photos of her dogs. She has a responsible, pretty professional job which could go either way, middle or working, but the other stuff I think defines her as working class.
My mum (my parents divorced) has her own home thanks to marrying well, as she has never been educated properly or done any job for longer than a few months. I think she is working class (despite not really working) but she thinks she is middle.
Her brother has a cafe/restaurant so is self-employed. He proudly tells people he never reads books, comfortably uses only the local dialect no matter whom he's talking to, and his hobby is going out with the local gamekeepers to shoot. Again it could go either way but the no books/dialect thing clinches it.
I sound like a terrible, terrible snob but I've only put this down because of this thread - they're all people, they're all great, I don't care, but those are my thoughts and a few examples.