While I was living over there (about a decade ago), people weren't using "England" to refer to more than just the smaller region -- it was "the UK" for the national identity. That may have changed, however; I don't know.
As for "America", it is not merely the Canadians who can be irritated. Latinos from South and Central America may also consider themselves American, and refer to US persons as "Norteamericanos" when they want to lump us with the Canadians, or "Yanquis" otherwise. Whether or not "Yanqui" is offensive probably depends on where you're from.
Update for clarity, 22-Feb-2008:
The phrase "depends on where you're from" wasn't clear, and I apologize. jonadab makes a good point about the southern point of view; but I come from southeastern Massachusetts. When we refer to a fellow New Englander as a Yankee, it's a compliment. When we talk about New York Yankees, it's a pejorative. The folks in Sussex, England called me a "Yank" while I was there, and I don't think there was any intended coloration, positive or negative.