The stereotypical English Accent (clipped, haughty, veddy veddy proper) is a very recent construct (not much more than 100 years). It's called Received Pronouncuation (or BBC English) and it was created for reasons of class. It was (still is) something that has to be learned and acquired. Americans think it is the natural way the British speak, but it's something they have chosen -- lower classes in England are easy to spot because they don't talk in RP. This allows the "best people" to easily recognize each other.
About the accent: I also remember reading that the American accents are more like earlier British forms.
Here is one example. Most Americans say for either "EE-ther." Most Brits say EYE-ther. EEther is the original way. The story is that when the English imported Wm.of Orange-Nassau as King, he (a German-speaker) misprounced either, saying it the way someone would read itb in German, and to make him feel comfortable, his courtiers imitated him. People outside the court imitated what they thought was proper, and the new pronunciation spread. It became established in Boston and other East Coast ports through contact with the latest British influences, and to this day is more common in those areas. The original way is EEther, and that is what Shakespeare (or Oxford) would have said.
I have always thought that the upper-class British accent was very sexy, especially in English women, who are among the best-looking in the world (IMHO). I was surprised to find that many English people are attracted to the American accent, and find it not at all irritating. I guess that it is what you are used to. I like the Irish people, but there are certain Irish accents, like that of the IRA spokesman Adams, which I find intensely irritating. It's the way it ends on an upward lilt for every sentence, as if asking a question, yet there is no question. Fortuntately, not all Irish people do that.
Regional accents in Devonshire and Somerset sound a lot like American English.