Let's Put this Battle of Britain thing in Historical Context..

[ElAurens]

Almost every war college in the world had done studies and simulations of the German invasion of South East England.

And in every case the German main force never gets across the Channel in sufficient numbers to create a sustainable beach head. Why? Because of the Royal Navy, and it has little to do with capitol ships. The German invasion "fleet" was well equipped, to cross the Rhine, not to cross the English Channel. The river barges that they were counting on were ill suited to use on open seas. RN destroyers and corvettes racing through the formations of barges basically would not even have to fire on them, as the majority would be swamped by the wake of the much larger ships tearing by at 30+ knots. The German units that did get ashore would be on their own, with no re-supply, little fuel, and no hope of retreat.

It never would have worked.