It isn't quite
right to say that the English of four hundred years ago sounded like a southern US accent, although for ease of reference it isn't too bad an example. The truth is that the accents diverged from a common source. If you go to the west of England you hear the same emphasis on the "r" but it certainly doesn't sound like a US accent. But our ancestors didn't sound like them either.
If you compare the two, you might get a reasonable idea of where the divergence occurred. Most of the differences between the US and UK (or England anyway) are easily identifiable. The short "a" in the US is more reminiscent of old English, since the long "a" was an affectation that arrived in the 19th century. It was interesting to note that in certain upper class environments in the US, the same affectation was also taken up.
Using the example of "gotten" is just another case of a word dying out in England, and continuing in America. It works both ways, until comparatively recently, the use of "twice" was fairly rare in the US, with "two times" being preferred, and of course, even in England "thrice" has virtually disappeared.
One thing more, there's no such thing as a British accent. The variety is far too wide to use such a term. You can get away with dividing it into English, Scots and Welsh, but not British. Think Billy Connolly and Margaret Thatcher, and you'll see what I mean.
She's as nervous as a very small nun at a penguin shoot.