The British stand a good chance of gutting the Kriegsmarine of its surface ships and experienced personnel. It is also likely that Germany will lose even more experienced aircrew and aircraft than in the historical Battle of Britain. I don't know what effects those will have on the rest of the war.
The Kriegsmarine was pretty useless anyways.
Seems pretty fantastical that the Luftwaffe is going to lose more aircraft fighting in the Channel than it did historically flying deep inland, and that the RAF is going to lose fewer fighting in the Channel with Bomber Command exposed to massed fighter attacks.
I've had ideas of doing a post-Seelowe story. I even have a title, The Sea Lion after Seelowe. (The Sea Lion being Churchill or Great Britain itself) My thoughts include a Great Britain that gets overconfident after defeating the invasion and attempt a landing somewhere on the continent.
What if they're arrested?