There was an story on This American Life a LONG time ago about southern accents in film and how bad they are. (The difference between life and "lahf" or time and "tahm". I consider English/British and American Southern to be the most closely related in sheer variety and geographical tells.

Depends. I'm from the southern part of Georgia. You wouldn't confuse me with an RP English speaker. Some of the rich, older families in town, perhaps.

We do have phrases in common, though. I'm guessing it's because the south was largely populated by Englishmen and we didn't get the immigrant explosion that New York and other major cities got in the early 1900s. My own ancestry seems to be 100% English.

Here is a nice quiz. I got an interesting result.

http://www.gotoquiz.com/results/what_american_accent_do_you_have