The Germans could not have successfully crossed the channel, its that simple. In fact the Kreigsmarine told Hitler this in summer 1940 after undertaking war games in Berlin.
The Germans did not in 1940 have any landing craft, and in late summer 1940 were desperately trying to buy up every barge in Belgium, Holland and France that they could. Self-production of landing craft had not even been commissioned.
Secondly, an invasion would have been destroyed by the Royal Navy. The RN was the largest navy in the world in 1940 by far, and much of it had been recalled to Southern England. They grossly outnumbered the German Navy and would have slaughtered any invasion crossing.
The RN in 1940 was strong enough that the Germans could have actually won the Battle of Britain, and the RN could still have successfully, with losses, stopped an invasion, despite lack of air cover.
Oh, and the Battle of Britain. I think that proves my point. A grossly outnumbered RAF defeats the Luftwaffe. The Nazis couldn’t win stage one of the invasion, let alone launch an army across the seas.....
Just my point. The English Channel is what saved Great Britain during WWII (along with considerable US aid). If the UK had been part of the European landmass it was would have been easily overrun by the Hitler’s panzer divisions just like the rest of Western Europe. This is my only point.