Answers to your question can be found in the FAQ.

Well since everyone is complaining so much about how "unhelpful" the FAQ is here are a few answers from the FAQ.

There are many, many evolving regional British and American accents, so the terms “British accent” and “American accent” are gross oversimplifications. What a lot of Americans think of as the typical "British accent” is what's called standardized Received Pronunciation (RP), also known as Public School English or BBC English. What most people think of as an "American accent," or most Americans think of as "no accent," is the General American (GenAm) accent, sometimes called a "newscaster accent" or "Network English." Source

So from the FAQ we can establish what we mean when we "American" or "British" English. Lets see what else we can learn.

In 1813, Thomas Jefferson wrote in a letter: "The new circumstances under which we are placed call for new words, new phrases, and for the transfer of old words to new objects. An American dialect will therefore be formed". As the settlers (including a good proportion of Irish and Scots, with their own distinctive accents and usages of English) pushed westward, new terms were indeed introduced, and these pioneers were much less reticent to adopt native words or, indeed, to make up their own. The journals of Lewis and Clark, written as they explored routes to the west coast in 1804-6, contain over 500 native words (mainly animals, plants and food). The wild “outlands” west of the Mississippi River gave us the word outlandish to describe its idiosyncratic characters.

Source

So it appears that distinct american words and phrases were already coming into use as early as 1806.

[Early Americans] saw western expansion as an excuse to expand the language with new words and quirky Americanisms like skedaddle, bamboozle, shebang, riff-raff, hunky-dory, lickety-split, rambunctious, ripsnorter, humdinger, doozy, shenanigan, discombobulate, splendiferous, etc, not to mention evocative phrases like fly off the handle, a chip on the shoulder, no axe to grind, sitting on the fence, dodge the issue, knuckle down, make the fur fly, go the whole hog, kick the bucket, face the music, bite the dust, barking up the wrong tree, pass the buck, stack the deck, poker face, in cahoots, pull up stakes, horse sense, two cents’ worth, stake a claim, strike it rich, the real McCoy and even the phrase stiff upper lip...

So clearly a large, new, American vocabulary was being developed within the first 20 years of the Nations existence and by the time Mark Twain began publishing it seems reasonable to conclude that American English had completely diverged from British English. So much so in fact that an Englishman and linguist named Henry Sweet (1845-1912) was convinced that "England, America and Australia will be speaking mutually unintelligible languages, owing to their independent changes of pronunciation”.

TL;DR American and English Accents diverged no later than 1806 when new words were entering into the american lexicon. At this time Anglo settlers had already had 150- 200 years to develop their own accents independent of the "English" Accent.

This is all from the FAQ as it is, you just need to apply a minimum of effort. This sub is a community and discussion, not a place for everyone to go to get quick and easy answers with no effort. Of course we encourage everyone to participate in this discussion and community but our standards come first, your need for convenience second.

For those complaining about the quality of the sub because of how many threads get "Nuked" that is what makes this sub unique, Bullshit isn't tolerated, everyone knows this (or learns it very quickly). If you are disappointed in the answers provided at times consider the difficulty of the question, this particular question is very difficult to answer with any certainty because people usually aren't very conscious of this sort of thing, especially before the advent of audio recording. Perhaps do some research of your own and make a meaningful contribution if there is an unanswered question you find interesting. There was a time when the Glorious and Beneficent WhoH8in was non-flaired you know.

I think this is more suitable for /r/linguistics.

So I suppose the answer the questioner (and myself) would be looking for is accounts or commentaries that first begin to discuss an actual difference in accent.

I'd imagine since the settlers of the new world took particular accents with them it would already be noticeable but what was the point when Europeans began to write of an "American accent"?

I remember reading something around the time of P.G. Wodehouse's writings that called the accent a fine pure instance of English but can't remember what it was. Anyone?

I've heard it claimed that the Appalachian accent is closest to the colonists. Is there any credibility to this?