That's the problem with historical dramas. If you make it completely accurate historically, today's audiences won't relate to it. If you want upper class characters to talk like actual Edwardian aristocrats, the audience would think they were all pompous, pretentious, and comical or villainous. It also happens the other way, though. It took a while for the upper class accent to form. Go back far enough and your aristocrats might have sounded more like peasants, and that won't do today either.
Old, upper class East Coast accents had a lot of British in them. They weren't always the same as regional accents. An upper class Bostonian, Philadelphian and Charlestonian might have sounded more like each other than like back country speakers in their regions. Maybe what we hear now as "British" was more the absence of strong American regional accents, than anything specifically British.