If the Germans had won the battle of Britain, and pressed their advantage in maintaining air superiority why couldn't they have just bombed the royal navy into oblivion? If ww2 taught us anything it's that air superiority decided the fate of navies. Or even brought up the italian navy to assist with whatever was left of it after the air campaign.
Wouldn't that have cleared the way for sealion?
Okay, here's why.
Dive bombers do not sink battleships.
...what, you wanted more?
Yes, air power was the decisive arm. But the times when air power was able to sink battleships tend to boil down to one of three cases:
The ship was at anchor, not under wartime conditions. (Believe you me, the Royal Navy nearly a year into the war is going to be under serious wartime conditions.)
The ship was hit by a highly advanced weapon from the late war, such as a Fritz.X glide bomb or a Tallboy. These weapons require a very specific attack path, and usually air superiority. And they've not been invented in 1940.
Or, the most usual case, it was LOTS AND LOTS of torpedoes. Torpedoes, not bombs - and the Luftwaffe sucked at anti ship work, and especially sucked with torpedoes. (Look up how much fire Yamato or Prince of Wales absorbed, and observe that they did not have any significant air cover - and it still took THAT to down them.)
Now, the more usual role of naval air power in 1940 was to find, harm, hamper and slow enemy ships. The idea is, if you have to face Bismarck when she can't steer, or she's lost a boiler, or she's just taken on a few thousand tonnes of water into her TDS, while your own ships are undamaged, then you will be able to pound her to bits more easily.
(The Stukas and Ju-88s, by the way, are the dive bombers the Germans have, and they're optimized for air support - not naval air power. The Germans did not do naval air power in any significant way, and they may not have even had much in the way of AP bombs. They are also needed for the landings themselves, because they fulfil the role of artillery for the arty-light tactics the Heer rely on and will need to do if they get ashore.)
So capital ships are, more or less, safe from the LW.
Destroyers, on the other hand, are vulnerable to LW bombs. But they're also much, much harder targets. (Consider the number of bombs dropped on the slowly moving destroyers at Dunkirk. Not many casualties. Hitting a destroyer is hard - and it's not until Crete that the LW seems to have got the hang of hitting moving ships at all.)
Cruisers are the middle ground. They can take a few bombs, but they might get hit by a few. Tricky.
What it boils down to is that the LW will, if it is able to do better than it did OTL, be able to sink... let's go hog wild and completely beyond the realm of plausibility, and say every aircraft carrier, one battleship, two battlecruisers, six cruisers and eighteen destroyers - thus making it the single greatest air power versus naval power victory in WW2 by a fair way.
Now, since Stukas are short legged, that attack will have taken place at most a couple of hours at flank speed from the invasion itself. (Assuming, that is, that the Royal Navy don't just make sure they reach the invasion area at night, because it's their choice.) In the time it takes the Stukas to land, rearm, get their aircraft serviced, and launch a second, inevitably smaller, strike (Inevitably, because that close to Britain the fleet will have air cover - indeed, if the LW is making a maximum effort strike, then there's nothing else for Brit fighters to do but shoot down Stukas over the Home Fleet), the Royal Navy has had at least an hour or two merrily blowing up invasion barges.
To prevent an attack on Great Britain is the reason the Royal Navy exists. If it looks like the invasion will be a success, they will throw everything that floats into the channel and not leave until they've each used up all their ammunition and then rammed things until their ships have fallen apart.
After all, England Expects.