The thing about an accent is that it will change over time, as new cultural and population shifts occur and with time passing.  In looking at the causes of the differences between American and British accents, the thinking around this is it was not the American accent that changed, so much as the British accents have undergone profound transformations in the last few centuries.  In fact the American accent, it is argued, stayed the same as the Elizabethan (or Shakespearian-era) English accent spoken by the first settlers of America, in the 16th century.
While the accent in America froze – but with a few changes along the way,  it was the accent in England as we know it that changed markedly.  In fact, many linguists claim that the language of Shakespeare works much better in an American accent.

The History of the American Accent

What we know from early sound recordings is that the American English accent in 200 to 300 hundred years was very different to the English accent.

Most of the difference lies in something “rhotacism.” The word rhotacism refers to how the modern British drop their R’s when pronouncing words such as’ barn’ or ‘farm.’

Most  American English still has the rhotacism, like old English. Many former colonists also adopted and imitated non-rhotic way of speaking English to show off their status. This occurred especially in the port cities like Boston and Charleston and across the south following the plantation culture. Some areas of the American Southeast, plus Boston, are still non-rhotic.

However with industrialization the new manufacturing hubs moved to other cities, such as Chicago and Philadephia. The next wave of immigrants to seek and make fortunes in manufacturing came from Northern England, Scotland and Ireland – and they also had rhotacism. Later on, the accent was shaped even further with the influx of German immigrants. That’s why there are regional differences in American accents all coinciding with which people the major immigrant settler population came from.

Meanwhile on the English side of ‘the pond’ as some called the Atlantic Ocean, it became posh in the Victorian times to speak with the accent you hear today in southern England. Following the upper classes’ example, in the 20^th century, other classes were soon imitating the accent. Civil servants, many of whom went to work in the colonies, the armed forces and then radio and telecommunications reinforced this way of speaking as ‘proper’ English.

There are dozens of evolving regional British and American accents, so the terms “British accent” and “American accent” are oversimplifications. What is thought to be a typical British accent is also known as BBC English. What most people think of as an American accent (or  what most Americans think of as no accent)  is the General American (GenAm) accent, sometimes called “Network English.”  Of course, with the speed that language changes, a General American accent is now hard to find in much of this region, with New York, Philadelphia, Pittsburgh, and Chicago developing their own unique accents, and GenAm now considered generally confined to a small section of the Midwest.

Watch this video about Shakespearian English and how English at the time would have sounded which is around the time of the discovery of the New World.

Or this one: The British vs the American Accent – a discussion on the Ellen Degeneres show with English actor Hugh Laurie.

With thanks to mental_floss!