There is only really the one british accent that's ever depicted in our media/whatever media makes it over here, so I'm sad to say almost certainly we do not.

That's why we only ever seem to imitate the one (or accidentally mix them, apparently). It's the only example we've got and we assume everything is that one. I don't know where any of those areas are any more than I know the sociological difference between them, and if I had to name any others, I don't know what I'd do.

Tomato still has mild southern variations ("tuh-may-duh/ter-may-der,") but it is a solid choice now that I think about it.