I think I'll find it's exactly as I said it was, at least as far as pronunciation and accent is concerned (which is what we're talking about). There was no such thing as an English accent until the English invented it well after the US was settled.
http://www.livescience.com/33652-americans-brits-accents.html
I've heard about that before. I'm not sure how true it is and there's no way to prove it as there was no way to record sound back then.
Received pronunciation would have only been used by the upper classes and while it's probably true some working class people tried to talk like that, it wouldn't have spread everywhere.
In the north, most English accents are non-rhotic but they pronounce the a in most words such as class and pass like the Americians do, p-ass, kl-ass, where as in southern England we say p-arse and kl-arse.
South western English accents are non-rhotic, they pronounce kart and smart in the same as they do in the US.
There are differences in British accents in the pronunciation of words containing the letter U. In most parts of the England tube, new, and and tube are pronounced, t-you-n, n-you, t-you-be, except in parts of eastern England, mostly Norfolk, Suffolk and Lincolnshire, where they say t-oo-n, n-oo, and t-oo-be, although this is gradually dying out.
In the north buck and book sound identical.
There are parts of the UK where this gets mixed up, such as in counties where different pronunciations diverge. For example in Northamptonshire a mix accents from eastern England, northern England and southern England are found.
Many people emigrated from Ireland to America so there are elements of Irish in US English.