Asia, I don't mean to point out a problem without putting forward a solution, so how about this?

http://en.m.wikipedia.org/wiki/Aksai_Chin

~Prestige: The British just gave you a serious drubbing in an actual war and signed Constantinople.
~Chance of easy diplomatic victory: There is no strategic importance and no ethnic British.
~Chance of easy military victory: No Indian conscripts, British have to ship every soldier and cannot blockade you. All for some patch of barren land.