Comments

When Americans (and many other foreigners) say "British accent" they usually are referring to RP, or the queens English as the "fake" accent here. Like many things it started with the upper class and proceeded down the ladder to those of lower classes wanting to emulate wealth and power to "pass" as higher status. As someone said the eastern americas would seem most likely closest, however the east was the center of wealth an drew power and followed British trends for some time (such as powdered wigs) so you can hear similar affectations to RP in some accents like parts of New England. Much like the cockney, the American south tends to have what is considered a "lower class" accent traditionally, and is unlikely close to "original British English." Because American regional dialects were heavily influenced by immigration especially in the early 20th century and late 19th, I imagine sorting it out would be tough.