I’m willfully ignoring nothing.
Royal Navy couldn’t defend British cities from Luftwaffe bombing.

And I’m not talking of surrender without invasion.
My opinion, and actually it’s not only mine, is that losing the Battle of Britain alone would have forced United Kingdom to accept a compromise with Germany.
Hitler would have conceded it gladly and without heavy conditions, just to have a free hand against Russia.

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 :)

You’re opinion is as good as mine.:) History can’t be changed.