People say Britain contributed nothing to the war? How about containing the German fleet in the Baltic, defeating Rommel (Yay Montgomery!), destroying a huge portion of the Luftwaffe over the United Kingdom, contributing to the D-Day landings and mastering the art of Night bombing over enemy territory? The British, along with the Americans, sent considerable supplies to the USSR, giving the Soviets much needed material aid. The British introduced a number of (then) revolutionary weapons like the Spitfire and Mosquito fighter/bombers, the Lancaster (arguably the best bomber of the war). The Spitfire was the inspiration for the P51 Mustang, the best Allied Fighter plane of the war. The British also retook Burma from the Japanese, beating them in their own environment.
Consider this; without Britain, North American (yes, both Canadian and American) would have had a very tough time opening the second front. Britain provided the allies a small but sure foothold and base in Europe, despite the attempts of the German U-boat naval arm to cut it off. Without the UK remaining free of German occupation, D-day would likely have never happened. Sure, the British had their asses handed to them in France in 1940 and in the Pacific for a while but they bounced back.
Prior to Operation Barbarossa, Britain and it's colonies (or commonwealths) were the only nations fighting Nazi Germany. The United States were not at war with Germany until December 11, 1941 and France had been formally surrendered on the 25th of June, 1940. Think about it. D-Day was in 1944. An effective liberation effort in Europe was not attempted before that (Italy doesn't count, that was invading an aggressor.) Without the British prescense in North Africa (and the Mediterranean), the German invasion of Africa would have been a matter of marching instead of an important campaign. For 4 years Britain resisted all invasion schemes or terror bombing attacks launched against it. It was because the British people continued to have a marvelous fighting spirit, even at the height of the Blitz.
Although, if it wasn't for simply Geography, we'd probably all be speaking German right now. The German army was the best in the world in 1940 and if it wasn't for the English channel (say Britain was connected to France via land) the invasion of Briton could have been a reality. Nevertheless, without the British in WWII, the fighting may have been much closer to home for us in North America and you in Iceland.
Man, this is the longest post I've ever written. I'm Canadian and I've been fortunate to never have been thrown into a war scenario but I find the world wars fascinating.