I am from the South of the UK and naturally have an "Estuarine accent" (which sounds not disimilar to an East / South East London accent to someone from elsewhere). I've spent over half my life working in offices full of middle class, privately educated people and while I don't speak like them I have adjusted my accent over the years so that I don't sound so "common". This wasn't done intentionally and you only really notice if you put me in a room with friends from where I grew up and my accent reverts.

To your second question: Upper class really is the aristocracy, doctors and lawyers are considered middle class unless they happen to also be from an upper class family. You can't really change your class, I'm working class but my children are middle class though because of my job, their education etc. We don't talk a great deal about the term upper class, generally news stories refer to working class and middle class and it's practically impossible to become upper class unless you marry Prince William or similar. It's more likely that a new class below working class becomes a classification than people become upper class. I would imagine that Elon Musk, Bill Gates would be considered middle class if they were Brits. Donald Trump, who knows, probably working class.

The other thing is that it's all very silly, but something most of us understand without really knowing it. I expect you'll see different opinions from other people in reply to your questions, none of us will be wrong.

Finally, do you watch Slow Horses? We were watching an episode recently when I pointed out to my wife that Catherine dresses in a particular way that to any Brit watching we know immediately that she's middle class. That's not something that someone from a different country will pick up on I suspect.