The United Kingdom of Great Britain and Northern Ireland consists of England, Scotland, Wales, and Northern Ireland. The Isle of Man and the Channel Islands are British Crown Dependencies but are not part of the UK.
The diner inside is not as seen in the show, but the sign is still there and there's local history behind it. There are framed newspaper clippings and the menu acknowledges the show's three waitresses: Alice, Vera, Flo and the owner: Mel.
I've lived in the Phoenix area for a long time. Never been to Mel's Diner. I'm old enough to have an awareness of Alice, the television show that gives the spot its ongoing notoriety, but I've never actually watched the show. Well, kiss my grits, as a character on the show used to say, Mel's is worth a visit.