Today, it is just the "educated class" which is full of working and middle class people (and foreigners) and dwarfs whatever genetically inherited RP population there was. This is a side effect of transitioning to (mostly) meritocratic admissions using the interview as a means of abstracting away the bias from expensive education.In the UK, there is a class of people who have an accent called "Heightened Received Pronunciation". Think Charles Dance from Game of Thrones.
You'll also note that your own example of Charles Dance was the son of an engineer (middle class) and a cook (working class) - I'm giving this as a counter example because of your reply to the "aristo" comment implying he was of more stereotypical birth.