'public school accent'

The accent of one who has been through the elite school system in the UK is distinctive. The question is -- how can this accent replace the original accent of boys from all over the country who presumably have developed their speech patterns when they get to school?

This accent is fairly rapidly disappearing from British, especially English, society. You only have to hear either Princes Harry or William to hear how current Public School characters speak - very much like lots of other people with what has come to be called 'BBC English'. However, this is changing too, with many regional accents to be heard.
Presumably the children do inherit their speeech patterns from their childhoods, but many are influenced by radio and TV programmes - see above.

Funnily enough, I've heard quite a few people with public school accents adjusting theirs to sound more common. Accents are more fluid than GB Shaw would have had us believe.