Flatly untrue.
"After the game's conclusion, the umpires unanimously concluded that the invasion was a devastating defeat for the German invasion force."
"Of the 90,000 German troops who landed only 15,400 returned to France. 33,000 were taken prisoner, 26,000 were killed in the fighting and 15,000 drowned in the English Channel. All six umpires deemed the invasion a resounding failure."
http://en.wikipedia.org/wiki/Operation_Sea_Lion_(wargame)
The biggest factors were the inability of the Luftwaffe to successfully engage smallish, fast-moving surfaces vessels such as destroyers and MTBs, even with air superiority. Against such forces, even with perfect weather, the Germans had no chance of adequately supplying any troops they might have landed in Britain.
It is more than a little silly to claim, based on staff operational plans, what Hitler was "planning to do."
General Staffs make plans. That's what they do. The US General Staff has plans in the drawer for invading every country on earth, including Canada. Or at least I hope they do. That's their job. Doesn't mean such plans are intended to be implemented.
In the final analysis, Hitler's plans for dealing with UK depended on the assumption that the British would give in or strike a deal so a full-blown invasion would not have to be launched, just as I said. He was shocked when they refused to follow the script. It had worked with every other European country (except Yugo, and the Germans had been able to squash resistance there in short order).
While the Army Groups had reached the shores of the English Channel in force, their logistical tail lagged far behind. It was going to take some very critical weeks before the logistical nightmares could be rectified sufficiently to sustain a major maphibious campaign into the island nation of Britain.
An amphibious invasion of Great Britain would not have been like Iwo or even Okinawa. It would have been more like Operation Olympic, the invasion of the Japanese home islands that thankfully never took place.
The larger the size of the resisting force, the larger must be the invading force to destroy it. Which requires proportionally larger fleets and logistics lift. The US Navy and Merchant Marine, after four years of the most aggressive buildup in history, would have been strained to the max to support Olympic.
Hilariously, Sea Lion was dependent on keeping the RN busy in the Med and Atlantic so the Germans could slip across the strait without RN resistance. As if the RN would not have defense of the Channel as A1 priority no matter what! If apparently wouldn't occur to them that defending the home islands might be important.
Could the Germans have taken Britain? Sure. But only after several years of using the resources of conquered Europe to build a fleet and merchant marine capable of doing so. Amphibious invasion of a large territory defended by a powerful and undefeated fleet and air force, and by land forces that are not insignificant is not something that can be improvised in a couple of weeks. It requires several years at minimum.
Had the Germans put their minds to it they could have potentially had nukes to use on UK, or they could have built a much larger U-boat force and starved them out. (Something that again would have taken years to build).
But nukes were largely out of their reach for the simple reason that the Nazis drove out or in some cases killed most of the people who could have built them, who instead built them for us, and U-boats as such were doomed by radar, to a considerable extent built by those same refugees from Europe.
So IMO the German war against Britain was doomed from the start, as far as invasion and conquest of the British Isles goes. Since any such notion was quickly abandoned by the Germans, it seems they agreed. Rather than putting resources into developing the ships they needed for an invasion of UK, they abandoned the idea completely and switched to a continental strategy of obtaining the oil and other resources they needed from USSR and the Middle East by land invasion.
Almost worked, too.
It would have worked if the Nazis treated the conquered Russians with some decency, in the beginning they were welcomed as liberators by many....of course the Nazis weren’t interested in making friends in Russia.