I agree with Andrew. Losing your capital will be important but should vary in its effect from country to country. I have got Stolfi's book on my bookshelf and he makes a convincing argument that the capture of Moscow was the move most likely to lead to the collapse of the Soviet Union but only if other objectives had been captured too. I think that COS models this well by saying that you must capture Moscow, Leningrad, Stalingrad and some other optional cities (Gorki, Sevastapol, Baku, etc) and this starts to accumulate Russian 'collapse points' which when they go above a certain level will cause the USSR to collapse. I think that worked well. For the Soviet Union to collapse just because one PzIII gets into Red Square seems a bit unrealistic but the capture of Moscow in its strategic and psychological impact would have meant something big.
As for the UK it could be argued, convincingly, that even if the UK had been captured the British would have fought on from the Empire, protected by the Royal Navy. Serious contingency plans had been set for this eventuality. Therefore the capture of Cairo (the middle east was seen as an alternative base in the event of the collapse of the British Isles) or even the invasion of Canada (getting into real 'what-if' land here!!) would possibly be needed. Actually, I hadnt thought of that. Sorry if I am asking something asked elsewhere or something that is in the FAQ, but can the Axis player invade the USA or Canada? What fun! If the Germans had defeated the USSR in 1941, knocked us Brits out in 1942 or 1943, it might not have been unrealistic (especially as this game seems to promise the potential to explore some real alternatives- ploughing lots of cash into a huge German navy, post-USSR collapse ala Z-Plan) for an invasion of America!!!