You guys are focusing too much on the narrow military application of force here. Had the British army been crushed at Dunkirk instead of escaped, there would have been precious little to stop the Germans once they landed. Without an army to defend , the British moral would have collapsed and the country would have folded. Once an enemy has been defeated in battle , the immediate next step is to exploit , pursuit and roll up the enemies territories, that would have included the UK.
Its one thing to defiantly resist while fighter and bombers duke it out overhead, its quite another thing to resist a combined ground & air assault. Comparisons with Normandy are invalid since the Atlantic Wall was a serious military boundary manned and backed by an organized 'battle hardened armed forces' with years of experience , and time to be ready for war. UK had none of this in the summer of 1940, after the fall of France. In the first phase of BoB , the RAF was fighting for its life and would have been too tied up defending its assets to intervene much or risk losing airbases and squadrons on the ground , thus ensuring RAF defeat. Of course German investment in Strategic bombers would have achieved a similar end too.
Like wise a major ocean sortie of German KM capital ships would have similarly tied up the home fleet , until after the invasion had begun. Concentration of German U-boats utilizing both mining & torpedo attacks, could have erected screens to prevent interference from the local 'anti invasion' RN escorts fleets , especially since these appeared to have been much more effective in the first years of the war.
The Germans could have realistically thrown a division over in each wave plus supplies for several months. When these ran low on fuel & food or vehicles, they could be seized from the locals as they moved along. Any one resisting would be shot....that seems to have worked well in Europe and would have worked just as well in the UK.
Invasion planning envisaged 2 day turnaround between waves of troops landing, but it would be more like a week turn around per wave. There is little doubt they could get the ships across, but there is considerable doubt that the Luftwaffe or RAF could sink that many boats, that’s just wishful thinking.
What ever British ships the Luftwaffe did sink during Dunkirk, was no where near enough to halt the flood of boats each way and neither air power could seriously affect the out come. ...and they enjoyed local air superiority at the time. Bombers of the time had a very hard time sinking ships. The brits got across 400,000 troops in a week during Dunkirk. “Combined arms” is the nature of this type of operation, that’s how it worked in Norway with land sea and air components simultaneously conducted, which would be a closer model than Normandy.
Yes there were only 10 operational KM destroyers /torpedo boats after the Norwegian invasion, but there were dozens of 'channel destroyers too . Had this been a part of the realistic prewar planning of the invasion of France , back in the 1930s, sufficient numbers of escorts and landing craft could have been fabricated in time to suite the mission. Historically as it became apparent that the lack of investment or planning left the KM with insufficient escorts, the burden shifted to a singular one dimensional attack from the air which is always doomed to failure. That was the key failure on the Germans part and probably cost them the war. Germany could realistically defeat the Soviet Union or the western allies sequentially, but not both at the same time.
If your the British or American , you have to seize theater air superiority first since that’s you method of attack. But if you are the Germans you do both a the same time. The Germans didn’t spend weeks defeating the Polish , French or Soviet air forces BEFORE they invaded…they just did it as a part of the ongoing operational plan. Combined arms are the name of the game and if sufficient planning had been invested from the start, it was doable. As it was historically, Hitler 'believed' he would not have to go to war with the UK and could cut a deal when the time came, which is why planning for UK invasion was not included. Clearly this was another one of Hitler strategic blunder.