Perhaps Glenn could furnish us with the appropriate statistics for what happens when light infantry fight destroyers.
It won't be pretty. RN destroyer captains were known for their timidity, so they'll hang about at the maximum range they can and fire off a few rounds before tossing the rest of their ammunition overboard and heading for home. Even if you somehow convince them to fight, what good will they do? Naval guncrews have no relevant training or experience for engaging land targets, so they can't be expected to hit anything, and even if they did the average shell only carries a kilo or so of HE - nowhere near enough to deal with troops dug in to the rolling hills and forests that cover the island.
Meanwhile, the light infantry will be shooting back with actual anti-tank guns. They're trained to shoot these at tanks, which are much smaller than destroyers, so they'll find it easy to place their hits for maximum damage, especially since destroyers are notorious for having little armour! The heavier guns and mortars will turn their attention from destroyer to destroyer in turn, blowing them apart with high-explosives they're absolutely unable to respond to.
The political shock will be immense as the RN is wiped out almost completely just outside its most famous naval base. With the armed forces unable to respond, panicked mobs will descend on London and demand the government make peace. I give them four weeks, tops, before they're forced to surrender, and that's if the Germans don't springboard off the Isle of Wight and take the whole country.
