How about the Atlanta Braves?
They're pretty much the oldest team in baseball, and their first BIG star was Hall of Famer Harry Wright- who was 'also' from Sheffield, England.
If not them, then the Cincinnati Reds. They 'claim' to be the same team that Harry Wright was an integral part of in 1869, but they're not...
Edit: Just for the record, I am actually NOT a Braves fan, nor a Reds fan. I'm a 'baseball' fan first and foremost, but my favorite team is the Phillies.