Most British people, when they attempt to do American accents, generally wind up sounding like movie cowboys to my ear. Actually, just one movie cowboy: It sounds like they should be addressing everyone as ‘pilgrim’.
The guy in their ‘master class’ recording likes to say ‘Louisianer’ when doing what I assume are Texan and southern redneck accents — I don’t think I’ve ever actually heard anyone say that.

Comments
Perhaps I am unobservant, but I never noticed that Anna Friel had a bad American accent in Pushing Daisies. I had no idea she was British.
They said “poll”, but who did they poll? Brits?
The original survey seems to have been this Radio Times bit. Anna Friel is both the #2 best and #3 worst, according to their poll of Radio Times listeners, while Hugh Laurie is both the #1 best and #4 worst. I’m not exactly sure what, if anything, that proves, except that their survey was flawed.
Anna Friel’s American accent is leagues better than Lee Pace’s English one in Miss Pettigrew Lives for a Day. They picked on the wrong Pushing Daisies cast member.