Drop tank capability allowed the Bf 109 to fight for a short time over London from the Pas de Calais, they wouldn't allow escort to Bristol or the Midlands. Twin engined fighters were poor at bomber escort, one large raid on a Birmingham factory may have had some success, it may also have been a massive wipe out, a repeat certainly would have been.
Below the distance Calais to Central London 160km/100 miles
An Me 109 at maximum cruise could fly 400 miles or 600 miles at economy cruise. Allowing 20% reserves, 100 miles for combat (probably only 50 miles at full combat power) and 20 miles for forming up leaves us an operational range radius of 100 miles.
Below the distance Calais to Birmingham/Coventry 320km 200 miles. With a drop tank adding 300L to the 400L internal fuel. We can probably operate at 320km or 200 miles from base so long as the drop tanks aren't dropped early.
As you can see the Luftwaffe stands no chance without a long range escort eg the the Fw 187 with DB601 engines.
The Kriegsmarine have radar. Do the Germans need to use barges at night?
If Sealion happens at the planned time in late September there's 11 1/2 hours of night for the Royal Navy to come out to play. The longer the invasion goes on the less daylight.
The Kriegsmarine had Seetakt radar on all destroyers, cruisers and battleships. FuMO 22 had about 6 degrees beam width and an operator could localise a target to within 1 degree.
No enough for blind fire but enough to illuminate with star shell or a powerful searchlight. Latter versions of Seetakt (late 1940?) received lobe switching and could blind fire accurately.
The German Army could avoid using its most vulnerable vessels at night.
The German navy had fairly good night optics due to more optically clear glass and multi coat optics that minimised internal reflections in multi lens night fighting binoculars. They'd still be outnumbered by the RN.
What aircraft does the Luftwaffe have to sink capital ships, do they have big enough AP bombs and torpedoes'?.
Good question. Its covered well on the NAVWEAPS website.
Ju 87 as dive bombers, Me 110 as slide bombers (quite accurate), Ju 88 as dive bombers and He 111 and He 115 as torpedo bombers. Do 17 as level bombers, probably throwing a stick of 4 x 250kg bombs from 1500m or so. Bombs fused for 5 second delay unless hard impact. If they hit ahead of the waterline they sink and blow up underneath causing more damage than a direct hit. The Me 109 could strafe. The British ships have very good fire control but the pom pom has bad ballistics and spoils this not solved till the boffors was used instead.
Of course by September 1940 I think the drop tank and bomb capable version of the Me 109E4B and Me 109E7B were turning up.
Much of the damage would have been done by light naval forces. A flotilla of motor boats and inshore trawlers armed with a WW1 3 or 6 or 12 pounder gun a couple of WW1 machine guns and maybe a few small depth charges would cause absolute carnage amongst the river barges
If they are amongst the invasion fleet the LW can't bomb or strafe them without killing their own men. A motorboat in the dark is virtually invisible. In daylight it will look like a German motorboat.
I imagine the Barges would have 1 or 2 sets of C30 or C38 20mm FLAK guns so not totally defenceless. German Torpedo Boats (about 900 tons) and e-boats would be around.
Again the Barges could avoid movement at night.