Battle of Britain
Air Battle England during Summer & Autumn of 1940
Battle for Britain
That's a different thing completely.
Winning the Battle of Britain doesnt mean surrender, you need ground troops to enforce capitulation.
Operation Sealion was never "serious" enough to be considered feasible even with Luftwaffe air superiority.
If you think Churchill would have said " Ok you have beaten us in the air, we wont fight you any more" you are mistaken.
Of course IMHO
