Here's something that's always stumped me: If the USA was settled by people fleeing prosecution from the British, why don't we (in present day) speak with British accents? All things considered, the US is still a "young" country - this didn't happen all that long ago. Did the language change that fast? Are the accents we commonly associate with places like Boston or New York City still "remnants" of the British accent?
we all should be really amazed that the British, Australians, Canadians, New Zealanders and all the English-speaking Caribbean nations can easily understand and speak to one another after centuries without the benefit of electronic communications and the great distances separating them. To wonder over minor accent and idiomatic speech differences seems to be niggling. All the native English-speaking peoples have no trouble at all understanding and speaking to each other. There are still remnants of the British accent in the Southeastern states, especially Virginia among the Virginia aristos, descendants of early plantation owners--the Virginia 'horsey' set ('Weekend polo matches') and also in the Carolinas.
It's probably incorrect to assume that the British accent hasn't changed since the USA was founded. It makes sense that different, divergent accents emerged over time. Whether the British used to sound American, or the American used to sound British; or more likely some combination of the two, it makes sense that distinct differences emerged over time.
What I'm saying is that all languages change all the time. If you take one language and give it to two cultures then over time the small changes each culture makes could add up to a vast discrepancy.