Since we are free today to consider the possibilities, suppose the United States had a standing army, air force, and the means to ship them to Europe, here is where England becomes critical.
First, let's look at the ramifications of a Europe without a free England. If the fall of France was a disaster since it meant the abandonment of the continent by allied forces, the loss of England would have been even more critical. Right after the fall of England, Germany would be free to sweep into north Africa and finish up routing out defending forces. Italy then could be tasked with watching the borders of the Third Reich while Hitler would be free to shift his might to the invasion of Russia.
Remember, the United States would have likely still been waiting to see what would happen at this point. With the full might of the German army pushing into Russia, the only unknown would be whether Japan would still attack Pearl Harbor, or if Hitler could convince them that the bigger picture would eventually get them what they want and more. Japan would have to concentrate on finishing their campaign in China in order to push into Russia from the east. Or, Japan would be tasked with holding while Germany finished Russia.
There are plenty of possibilities and they hinge on many events. Instead of continuing down this path, let me get to what can accurately be surmised with the fall of England IF the United States were someone ready to attack Germany.
Without English bases, the United States would have had to ship forces to somewhere in Africa without the protection of the Royal Navy and Royal Air Force during long Atlantic crossings. Without England, launching an assault on France would have been impossible, so the U.S. would have to settle for creating a single front in Europe, likely coming in Italy. Before Italy, Africa would have to be secured, before Africa, the Atlantic.
So now, you see the problem.
Another tangent: Perhaps the United States would have had to work its way from the Pacific, battling Japan across the ocean, through south east Asia, and into China. Joining forces with China they would attempt to retake Russia who likely will have fallen to the concentrated - and undivided - German might. But then, what difference would hundreds of thousands of Russian and Ukrainian soldiers conscripted into the German army make for a land campaign. Have no doubt, fighting a war in Russia is a bad idea for anyone, including the 'good' guys.
No, more than likely, if England had fallen, the United States would have had to enter into treaty with Germany. An uneasy piece while we (or they) develop nuclear weapons. But then, if we had the bomb, where would we use it? On Paris? On London?
With the stakes set, enter the Supermarine Spitfire.
The battle lasted only three months, but during that time, over fifteen hundred German planes were lost, the numbers of equipment and men never to be recovered. One must always keep in mind that these were combat-trained airmen, going up against volunteers, and the best of German engineering going up against manufacturers who were unknown outside of air races.
An interesting irony, given the outcome of the battle, is that while Germany continued to underestimate the size of the RAF and Britain's production capacity, which gave them the impetus to launch more and more daring and violent raids, England continued to OVERestimate German strength and production, which caused them to develop a strong defensive strategy. So, while the battle raged on, Germany felt they faced an enemy that would surrended at any time, while England saw an enemy that had to be waited out.
An excerpt from Hitler's directive brings a whole new meaning to the courage shown by the English military and people:
Since England, despite its militarily hopeless situation, still has not shown any signs of being prepared to negotiate, I have decided to prepare a landing operation against England and, if necessary, carry it out. The objective of this operation is to eliminate the English home country as a base for the continuation of the war against Germany.
By the numbers, England should have surrendered. They too were seeing appalling losses in the skies, and, German bombing raids on London, designed to break the moral of the people, were truly devastating.
Thank you Mr. Mitchell.