@talk72000,
To a certain degree yes. There was a programme on television a while ago about German audio tapes of British POW's from WW1. There was a recording of a soldier from Surrey. Today a Surrey accent would be described as 'posh,' or estuary English. The recording though was quite 'oo arish,' and today sounded more like the English spoken in Somerset. The English spoken by WW1 soldires from Somerset was even more pronounced.
I think Shaw was more concerned with class and social mobility than anything else. Pygmalian is a bit like Trading Places. Also Henry Higgins doesn't give himself a real challenge. Eliza Doolittle is obviously from the East End of London, and the posh women he talks to at the beginning of the play are all the same class and set as he is.
Geographical mobility and parental background play a large part. I'm a real mixture. My parents are from Yorkshire, and I spent a lot time time there as a kid. I was born in Kent, I moved to Southampton when I was 14, then to Newcastle -upon Tyne when I was 16, and now I'm back in Southampton. My accent tends to vary depending on who I talk to. I spent so much time having to listen to different accents as a kid , and having to imitate my surroundings to fit in that now I do it without thinking.
It can be a bit awkward on holiday, particularly when a 'geezer' from Fulham who I'd been talking to earlier in a cockney accent finds me 'Ha waying the lads,' with a Geordie at the bar. Someone always thinks you're taking the piss.