A few observations. There has been some comments about the capability of the Swordfish, and how it was only effective against static targets. This is patently untrue. Stringbags and Albacores were used very effectively against moving targets, the most famous of which are Matapan, and the operations against Bismarck. Less well known is the virtual domination of the Central basin by the airgroups of just one or two carriers, until the arrival of FleigerKorps X in January 1941. until that point the British had wrested the complete initiative off the Italians (and no, the Italians were not a bunch of cowards who didnt want to fight, its just that the carriers gave the british such an overwhelming advantage at sea that the italians could not risk an open confrontation). in that time they had sunk a number of warships, as well as over 250000 tons of merchant shipping, helped to immobilise an entire navy (the french fleet) and suppressed the activities of another (Supermarina)
Unique in the worlds airforces at that time was the ability of the British carrier groups to hit with pinpoint accuracy targets at night. The strikes against Taranto, Bismarck, Sardinia, Genoa, Tripoli, Matapan, and many other places were all delivered in the dead of night. And this was not a case of a four engined bomber lumbering blindly around the sky trying to find an entire city, the RN FAA demonstrated time and again the ability to find, and hit, very accurately individual ships of all sizes, in the dead of night. They had spent years in the prewar period training and developing the techniques needed for such operations, and in 1940 they were a truly unique group of men completely overlooked in the modern observations, because they operated so differently to the more flashy American and Japanese air arms
In the case of an invasion, one has to assume an RAF badly wounded, and forced to withdraw to the midlands, but one would also have to assume a Luftwaffe also heavily wounded, and unable to dominate the sky to quite the extent it had over Europe up to that time. There could well be opportunities for the FAA to land its a/c on undamaged land bases, or undertake fast carrier raids at night, with devastating results. The barges earmarked for invasion were capable of a sea speed of 2 knots, the distances to the nearest debarkation points was over twenty miles. thats a travelling time of at least ten hours, but when one factors into account the effects of tides and currents, the travelling time for each journey is going to be in the order of 20-24 hours. Then the barges have to unload, if the the Normandy experience is anything to go by, these transports attempting a beach landing (sometheing they are not designed to do), are going to need something like another 24 hours to unload. So the RN, for each transport that leaves France, is going to have a massive window of opportunity to deal with that transport, probably in the order of 36-48 hours...time enough to pound it with everyhting the RN can bring to bear, destroyers, MTBs, night flying FAA a/c, mines (something frequently overlooked...there were mines applenty off the British coast, and the germans were not adequately prepared for this threat) day bombers (less impeded by the LW because of the losses to the German fighters the same as the RAF fighters).
The invasion would have been a disaster for the germans. The professional officers organising it knew this, both from the army and the navy. It was organized half heartedly because the germans had no experience in amphibious warfare (Norway was not an amphibious invasion, it was a surprise landing party on a gigantic scale)
Laslty, a word about German aeronaval capabilities at this time. The Germans did have a specialist air unit at this time, and it had proven itself very effective. It was FliegerKorps X, but in the late summer of 1940 it was not operationals, it was recovering from the losses it had suffered over Norway. When the Germans had tried to use non-specialist units in the maritime role, such a their attacks against the channel convoys, and against Dunkerque, they were generally unsuccessful. It is untrue to say they were completely inneffective, but they were certainly a lot less efficient than the specially trained units, which were simply unnavailable because of losses at that time. Against fast moving destroyer forces i dont give the german non-specialist forces much chance of a hit. The level bombers wouold have been more or less useless 9the germans had no torpedo equipped units at this time, and their divebombing capabilities were very restricted. that left the Stukas, and the bomb carrying Me 110s. a Stuka carrying a bomb is fairly short ranged. An Me 110 operating as a Fighter bomber is more long ranged, but unable to be escorted, and therefore vulnerable, even to a skua or a gladiator.
I just cannot see how the Germans could hope to pull off the invasion with any hope of success.
Having said all that IMO it was the RAF that won the actual battle its just that ther was some doubt about the ability of the RN to influence an invasion, if the need arose