If you want to get a good flame war going on an alternate history forum, the easiest way to do it is ask what would have happened if Operation Sealion had been launched in 1940? There are, alas, many newcomers to the field who see Sealion as the great missed opportunity for Adolf Hitler to win the war and don’t grasp that Sealion, far from being a simple river crossing, would have been an incredibly difficult operation and the odds of victory would have been extremely poor. Kenneth Macksey wrote a campaign history of a successful Sealion in 1980 (Invasion; a condensed version is included in The Hitler Options(1995)), but a wargame that was carried out at Sandhurst in 1974 concluded the invasion would have been a complete disaster. Even with matters heavily and unrealistically slanted towards the Germans, they still lost. This wargame was later dramatised as Sea Lion (Richard Cox 1974).
This is not immediately apparent to newcomers, and it can lead to bitter resentment when a newcomer, posing an innocent question, is swarmed by dozens of more experienced alternate historians who have heard the question so many times they are thoroughly sick of it. I know quite a few prospective newcomers who felt they were driven away, rather than having the question treated seriously, and allowed bitterness to destroy their interest in something that once called to them.
The problems facing the Germans were immense. Britain was probably at her weakest in July 1940, and even a small German force making a successful landing might be enough to force the government to sue for peace, but the Germans would find it incredibly difficult to land even a handful of soldiers. The Germans had done almost no planning for an invasion of England and, more practically, lost considerable amounts of men and material in Norway and Holland. The shortage of transport planes alone would be enough to put paid to the German plans. It is possible, of course, to postulate a timeline in which Germany chose not to invade Norway and Holland, stabbing straight into France rather than the low countries, but that would have other effects. There would be, I think, much less confusion in France if the Germans proceed with their original plans for war. The downside of this, of course, is that Chamberlain would still be Prime Minister and, while he wasn’t as weak and foolish as he is often portrayed, he lacked the backbone he so desperately needed.
Germany’s window of opportunity, as tiny as it was, rapidly closed as Britain recovered from France’s fall and prepared to continue the war. The Germans could not drive the Royal Air Force out of the battlespace, nor could they rely on submarines and aircraft to sink the Royal Navy. Their ability to land troops was very poor, dependent more on makeshift barges rather than proper transport ships. Each month saw Britain growing stronger, with more and more anti-invasion defences in place. The British army was not yet capable of taking on the Germans on equal terms, but it would not have had to. The invasion force would be in shambles before it even landed on British soil, the men seasick and the panzers rapidly running short of ammunition and fuel. By late 1940, even Hitler conceded as much and directed his attention to Russia instead. In doing so, I think, he avoided a defeat that would have changed the course of history.
This does not, of course, stop writers from speculating on what might have happened if Hitler did invade and occupy Britain. Nor should it.