Interesting..... this works the other way around as well. I am a Brit living in the US for 17 years now.
Americans can usually tell I am from England, but have often thought Australia, NZ, S.Africa (Ireland -rare, and Atlanta, GA !!!?).
Over in UK, they typically can recognize the accent, but I think are slightly thrown off by my phrasing, and word choices - I am sure I have picked up lots of American ways of saying things.
I sometimes feel a bit "mid Atlantic", a strange feeling hard to describe.
H