As to the individual nations, I was surprised to hear that athletes from Northern Ireland were competing under the rubric "Team GB." It would seem that it's GB and not UK specifically to exclude them.
See, I see that from completely the opposing perspective. Officially, the country is called "The United Kingdom of Great Britain and Northern Ireland" so to my mind the adoption of "Team GB" seems more exclusive of NI than "Team UK" just because of the wording in the country name.
That said, I've no idea why "Team GB" is the preferred name...I guess because it's more natural to say that we're British than UKish or UKers (which leaves itself open to casual obscene mocking!)