This isn't really an answer, but more of a clarification, I think...

So accents are part of what makes up a dialect (other parts being vocabulary and grammar), which is simply a variety of any language used by a subset of speakers. English has many dialects within England (Cockney, West Midlands, Received Pronunciation, etc.), let alone the rest of the British Isles (e.g. various forms of Scots English or Irish English) and the wider English-speaking world (e.g. Jamaican or Indian English), just as American English has many dialects (e.g. Southern English, New York English, Boston English, Cajun English, African-American Vernacular English, etc.). What you're probably asking about is "Received Pronunciation" a.k.a. "The Queen's English".

So I think the proper question(s) might be: What is the history of Received Pronunciation? or What is the general history of the linguistic evolution of English dialects in England? or How similar or different were the "standard" - so far as there were any - dialects of English spoken in England and the American colonies at the time of the American War of Independence?

I would also highly consider cross-posting this to /r/linguistics or a similar sub, as this sort of question is right up their alley.