RN preparations to repel the German cross channel attack are generally not commented upon, I suspect because most of the armchair generals pedalling the idea of a successful cross channel invasion don't want to bring out just what an impossible task DKM was facing.
The RN had between Plymouth & Harwich ( i.e., less than 8 hours sailing time from Dover) 1 Battleship, 1 Town Class Cruiser, 4 Light Cruisers, and 44 Destroyers. Not included in these figures are a further 13 French, Dutch, & Polish Destroyers and Torpedo Boats also in the same area, operating under RN direction. There were also about 450 armed auxiliary vessels (gunboats & armed trawlers etc) also available, armed with weapons of 4in caliber or greater. There were about 30 MTBs and roughly twice that many MGBs and Fairmile type MLs. In total, the RN would have access to about 1000 surface combatants within 8 hours steaming of the invasion beaches. You can basically double that number if the entire british isles is included 9with a maximum 2-3 days steaming time). Many of the vessels were attached to western approaches command, but many others of the escort type vessels were not suitable for open ocean work. They had been raised 1939 basically to drive the U-boats away from the vulnerable coastal regions of the UK and were being employed in this capacity at the time of seelowe.
The northern diversion by larger units of the German Navy was actually Operation Herbstreise, and was part of the 'real' German plan. The only three operational German light cruisers ( Koln, Nurnberg, and the old training cruiser Emden ) were intended to escort a number of liners, including Europa, Bremen, Gneisenau & Potsdam, together with 11 smaller vessels, towards the east coast between Newcastle & Aberdeen to suggest that landing were imminent there. At the same time Hipper, assuming that her faulty engines did not let her down, was to operate near Iceland. These dispositions were intended to distract the Home Fleet from opposing the real landings. However, as the Admiralty never intended to send the Home Fleet south anyway, the relevance to Sealion would have been nil. Having said that, if the diversion force was intercepted by the Home Fleet, and this was a distinct possibility as the ships needed to ensure that the British spotted them, then DKM could well have lost its few remaining operational larger ships, as well as some prestigious liners.
Some Pro-german sources have suggested that HOOD and ARGUS would be rushed south as part of the Sealion reaction. The idea that the 'thin skinned Hood' & Argus would have been sunk by the Luftwaffe is also very far fetched. The Admiralty had no reason to commit ARGUS, and HOD, whilst thin-skinned vis-a-vis other capital ships, was certainly well enough armoured to resist the kind of bombs available to the Luftwaffe in 1940. In fact, in the whole of the war, the largest RN warship sunk by the Luftwaffe was a CL
There was some planning in DKM to use super heavy artillery based on the French occupied territories to seal off the channel in some way. I find the idea that coastal batteries would have sunk or badly damaged one or two battleships or an unknown number of other ships as frankly absurd. The coastal batteries were quite amazingly ineffective. As examples, on 29 September 1940 the monitor EREBUS bombarded Calais. Whilst withdrawing at her maximum speed (8 knots!) she was fired at by the vaunted coastal guns, but unhurt. On 11/12 October, 1940, the BB REVENGE, together with the 5th Destroyer flotilla, shelled barge concentrations at Cherbourg, She was fired at for some time by the guns behind Cherbourg as she returned to port, but again was not hit. Hitler ordered that the coastal batteries 'must dominate & protect the entire coastal front area' but saying a thing doesn't make it so!
DKM warships amassed for the invasion ran to the following:
In the summer of 1940 the only major surface units available to DKM were CA HIPPER, CLs KOLN and NURNBERG and EMDEN, and these were all assigned tasks with the diversionary forces.
For the invasion DKM had 7 full DDs and 12 largish TBs, 21 S bootes, 5 R Boote flotillas (roughly 30 boats) and 7 M Boote squadrons (about 28 boats). Most of the MSWs were of the large and capable M class type weighing in at about 650 tons . & sperrbrechen were assigned to the escort group for the invasion. DKM had available about 35 vorpostenbootes essentially armed trawlers
In terms of sheer numbers, the RN has the advantage hands down. The 100 or so escorts available to DKM would be met by up to 1000 RN coastal vessels. Probably the sheer numbers of vessels involved might initially prevent the RN from getting to the 2400 invasion barges assigned, but with that many ships attacking the invasion fleet, it would only be a matter of time before the RN was tearing into the barge groups. The 1974 wargame of Seelowe carried out at Sandhurst by German and British veterans was never able to successfully get the invasion forces across the channel, so in the finish it was agreed simply to land the German forces 9disregarding the naval battle to see what might have happened anyway.
Certainly the Germans assembled 2400 barges, but even the powered ones were incapable of making the crossing unaided. The barges were to be towed in pairs, which would have been fine had the Germans been able to provide sufficient tugs, but with only around 550 or so, they were already desperately short, before inevitable losses are even considered.
Finally, an invasion in Mid-October. As 11 days were required simply to get the first wave ashore, it would have been a brave, or foolhardy, German meterologist who would confidently assure his fuhrer that the weather in the Channel in October & November would remain calm enough for invasion purposes. In any case, the loss of so many barges from the inland waterways had seriously disrupted the German economy, and the need to release some, at least, had become acute.