The BoB is always an interesting theme, now isn't it!
What stands unmentioned here is that the mighty LW lost some 1.200 aircraft together with crew in a timeframe of just a couple of months. It was their finest. The RAF lost what 800 aircraft or so, and some 400 pilots.
This is a remarkable feat, and the LW hardly ever had so much blood drained from them (if you also include quality, and relative size) in WW2 at all!
When the thing was over, the LW could not mount anything like this against Britain in daylight. Never again.
And it drew some punch out of them when they went on about the deal with the USSR!
Then the debate, - was this what stopped an invasion of the British isles? Or was it the RN?
IMHO both. Well, the RN had been and was at the time the biggest navy in the world. So why the concern of aircraft vs the navy, especially when the Dunquerque losses were not so high...?
Here I have to slightly disagree with Milo. While the Dunquerque losses were low, RAF activity over there was quite some, with interceptions over France. Wasn't it over there were Robert-Stanford Tuck had a 5 kill day?
The Barge pulling was supposed to happen at night, with the beach landings at dawn. That gave very little time for the home fleet to engage, but some, as well as air attack and beach front issues as well. It was crucial to have absolute air superiority, only then could this even be attempted.
And where was the LW at the time where the descicion was taken to cancel the invasion?
1000+ aircraft & crew poorer, facing a bigger RAF than they ever had before, as well as finding out that the RAF was indeed NOT only in the south. The LW who had expected to wipe out the RAF in less than a week!
The Germans tried to established air superiority and failed. They tried to bend the British as well with big bombings, and they failed. A sequence of many interesting things lead to this results, and intelligence as well as moral and politics also playd a big part. But a big part was the performance of the RAF as well as Dowding's system. It was a chessgame and the RAF won it by "pawn"