The Puritans were a protestant religious group that held many similar beliefs to modern day anabaptists. They were persecuted in England and went to Holland where they enjoyed the religious freedom of the day. Children were born in Holland and they picked up on the dutch accent and style of speaking.
Eventually, they made their way to the new world, and as time went on, the settlers had a distinctive accent and way of grouping sentences and pronouncing vowel sounds that was different from British English.
The "posh" style of British speaking didn't even form until the Victorian age. I don't want to get too into it, because I don't know much about British history compared to what I know about American. I'll leave that to the Brits to tell that story. But what I have read is that it was a way for royalty, nobility, and landed gentry to distinguish themselves from the lower classes. It was called "Received Pronunciation" and it was taught in schools.
One interesting thing is that by studying old poems, linguists can figure out what words rhymed together. They have determined that in the first millenia, the English spoke with a rhotic "R" sound, which means they used hard "R" like Americans or Irish do.
Also many have determined that the English accent of the seventeenth century sounded much like the modern-day Boston/New England accent.
And then all that wonderful melting pot of German, Irish, Spanish, African, Native American, and French people living together in different areas, all mixed together in that exciting American mestizo has developed our regional accents and cultures.