"It's a way of speaking that is all tied up with the Old Country, the Queen."
This is rather disgusting--this country fought a war to sever familial ties with the UK. Read the Declaration of Independence (or especially the first draft).
Now pushing that aside, personally find a lot of British accents natty (if natty can be used for accents), except for pronouncing it is/it isn't as it tis and it tisn't. It does seem to have an air of formality about it. However, it is as ludicrous that those with British accents should automatically be considered intelligent and refined as it is for those with Appalachian accents to be considered uncultured idiots.
There can be unintelligent, boorish Britons and cultured and smart Appalachians--and of course the other way around. Opinions about the behavior of a man shouldn't be determined by his accent (which isn't the same as his diction).
P.S. Wouldn't be that much against it if the media changed from "standard" American (media-American English) to an American "Received Pronunciation." But keep the proper (American) spelling and words such as truck, wrench (the tool), elevator, etc.
Before waxing too lyrical about British accents go to London, ride around on the busses and Underground and listen to the chavs talking among themselves.