Interesting points, Foolestroupe. The cracking of both the German and Japanese military codes in the war was crucial to Allied victory. Funny that neither one of them caught on to what was happening... (Hitler eventually began to suspect it, but far too late. That's why he insisted on complete radio silence prior to the Ardennes offensive/Battle of the Bulge in Dec 44. They achieved surprise that time, but by then it was about 3 years too late to make any real difference in the outcome.)

I would suggest that it was not necessary for the Germans to physically occupy the British Isles in the '40s in order to technically win a war with England. They would merely have had to win big enough in the Med, North Africa, and the Middle East, and hurt the British Empire economy sufficiently to get the British to talk peace terms....not a surrender...just a cessation of Anglo-German hostilities and a negotiated agreement on what to do next in western Europe and the Med, etc. That, I believe, they could have arranged, because the UK is nothing if not 100% pragmatic when it comes to insoluble dilemmas such as wars that have become unwinnable. They negotiated an end to the American revolution, after all. They have pulled in their horns after other military fiascos that didn't go well.

Given the fact that Hitler envisioned the British as his natural allies, I think he would have been quite eager to negotiate a "live and let live" mutual arrangement and not invade at all...as long as it appeared feasible.

His next hope would then have been to get the British onside to help him fight Russia. And it's just possible he might have succeeded in that, specially if the British were offered some territorial gains out of it...say moving up from India into Afghanistan and southern Russia.

That would have realized Hitler's dream of Germans and Anglos running the world.

The British are practical people. They would have done first what was necessary to survive....then the next logical thing that might restore their strength and influence on the world scene as soon as possible. If that had meant working with Germany in the 40s, they would have done it, in my opinion. Maybe Churchill would not have, but his successor would have. Churchill would have gotten sacked in such a case.