If England had fallen before the Americans entered the war, the Americans probably wouldn't have gotten involved in a war in Europe. Where could they have staged a "liberate Europe" invasion?
Iceland would have been the closest point. Otherwise you're looking at fighting your way up Africa to a place where you can launch Operation Torch (the invasion of Free French North Africa) and going from Africa to Italy, somehow hoping that Free France would let you through those mountains.
As for the Royals, etc - they would have fled to Canada. There was already a plan in place where there would a joint US/Canadian defense of Canada (the Americans didn't want the Germans to use it as a staging ground) - and possibly the Dominion of Newfoundland would have been included in that. Many of Britain's treasures had already been moved to Canada for safe keeping and the remnants of the Royal Navy would have based in Halifax.
There was a "we've been invaded - go to the prepared resistant points" plan in place in Britain. Carefully hidden arms caches, underground camps - that sort of thing - with every trained resister vouched for by the head of the local police. Which meant the first thing they were to in the event of invasion was shoot the one man who knew all their names.
http://en.wikipedia.org/wiki/British_anti-invasion_preparations_of_World_War_II#Plann ed_resistancehttp://en.wikipedia.org/wiki/Auxiliary_Unitshas more information on that subject.
Things could have been different - very different - and we owe a debt to all the boys who never came home. They're the ones who made this world what it is.
Goodgulf