That's a great link, chuckfickens- thank you. I hadn't heard the term British Islands before.
http://upload.wikimed...er_diagram_15.svg.png
I think our Olympic team covers the British Islands then plus some overseas areas (British dependencies?)
They're British Overseas Territories, and have been since 2002. At least four of the fourteen have their own Olympic Committees. Some of the others have no permanent non-military inhabitants and would not enter an Olympic team. I assume the remainder are allowed to take part as part of "Team GB".