You're right, they didn't capture them, they bombed the crap out of them and harassed them to death while trying to cross the channel. Hitler was still 100% capable of crossing the channel after Dunkirk, had he focused his Luftwaffe attacks more on British Airfields, as apposed to the civilian population, there isn't a doubt in my mind that they could have crossed. They could have crossed anyway, (although it would have been highly pherric if they did not try to destroy the RAF) and would have destroyed the British.
Gibberish.
And yet not, - this period marks a significant change in thecompletely so-far-successful Nazi campaign.
Hitler could not stop the crossings of several hundred thousand men floating away in just about anything that would .... float. And the LW actually suffered quite some casualties over the land they held.
And while the British airfields in the south were indeed buckling under the weight of the LW, don't make the same mistake as the Germans. They thought ALL of the BRITISH airforce were fighting them and rapidly depleting. They were bleeding every bit as fast themselves, and absolutely failed to comprehend the structure of the British air power.
After all, RAF had Bomber command and fighter command, and fighter command was basically split down in 4 in homeland defence, only 2 of which were effectively defending the south. 10 and 11th group. 12th group didn't make it to the fray before the Germans reached for London. 13th group was relatively idle up north and in Scotland , but did baffle the Germans when they sent bombers on that flank over the North sea, expecting all the British being in the south.
Then there was Coastal command, and the Fleet air arm as well. Not having quite the fighters for tackling the LW, they had quite some skilled pilots. Both arms were rather idle in the fight.
In the BoB the British had planes and crews in odd places. It was in the summer of 1940 when they for instance caught a German submarine with all hands with an aircraft of a squadron operating from .... Iceland.
The tactics and success debate is still warm, but I think I may claim that both sides did lot of mistakes. It would have been almost an impossible feat for the Germans to deliver a K.O. to the RAF though, and with the RAF around, the RN could not be stopped. Both depended on one another. Britain on both. And to hold the RN at bay, the RAF had to be held off. Didn't work.