This is an extraordinary claim, that doesn't seem to have been fully addressed. Though
@Big Nev does point out one major difficulty of using subs:
The Deutschland class subs existed in WW1. They were large "merchant subs" designed to carry cargo, and could indeed carry around 700 tonnes. I can't see any evidence that Germany built anything similar in WW2.
The 20-40 subs at sea the whole time in 1940 that you refer to must be type VII? I'm no expert on the Kriegsmarine, but I can't see any reference to other types of subs that were operational, but correct me if I'm wrong.
A type VIIA had a surface displacement of 626 tonnes, and up to 745 tonnes submerged. I guess you know how that works, that the sub floods some tanks that are full of air. The water is heavier, and causes the sub to sink. The more water in the tanks the deeper the sub goes, but not to sink uncontrolled. The deeper the sub is, the greater the water pressure on the vessel. So this balances out and causes the sub to float at a specific depth. For a type VIIA to a maximum depth of 220m, ie. with the tanks fully flooded and at maximum displacement.
What do you think happens if you load 700 tonnes in one of these subs?
First, this means the sub doesn't have enough buoyancy to ever float on the surface. You could support it in some way while loading it, but it would immediately sink when released.
Second, it couldn't come back up. Normally the subs force air back into the tanks to remove the water, reduce the displacement, and the water pressure pushes it back up. But with the tanks FULL of air the sub needs to weigh around 625 tonnes to surface. It would weigh 1325 tonnes.
Third, rather than just going deeper, the water pressure becomes too much for the hull. At around 230-250m the sub implodes, catastrophic hull damage occurs and the living quarters start to fill with water. The sub becomes even heavier and sinks even further. Even in the deep ocean it will go to the bottom - it's soon just a lump of metal with no buoyancy at all.
The later type VIIs were bigger, the VIIF had a surface displacement of 1084 tonnes, and a maximum submerged displacement of 1181 tonnes. It's obvious that none of these were designed to carry more than a couple of tons of cargo. For instance by reducing their fuel and supplies (and therefore their range), they could replace that with something else. The biggest weight reduction could probably come from not carrying any torpedoes and mines. A type VIIC (first built in 1940) carried 14 torpedoes and 26 mines. My rough guess is they would weigh less than a tonne each. So maybe 30-40 tonnes.
But then comes the other problem - where do you store the cargo safely? The Deutschland class were built with cargo compartments, type VII's weren't. Nor were they designed to get loose cargo in and out of the sub very easily, I assume they can be loaded/unloaded only in proper dock facilities. Over a beach?
Yes, Germany could have planned to build some larger subs designed specifically to carry cargo. Again a strategic re-allocation of resources away from tanks etc. when there was no long-term strategy to invade UK specifically, and generally no intention to develop either an amphibious assault capability, nor an ability to supply an army overseas. For example, they relied totally on the Italians to supply their forces in North Africa. And if you were going to use a surprise amphibious assault, then there were surely far more favourable conditions to do so in July 1941 in the Baltic as part of Barbarossa. They had another year to prepare, and no where near the threat of the Royal Navy and RAF.
BTW - on the idea of a surprise amphibious assault of the UK, one word: ULTRA.
I can't remember if the open wargames that occurred in the 1970s by Sandringham occurred before it was publicly acknowledged exactly how much the UK government knew about German plans from interception of Enigma encrypted messages. Anything you read based on information available to historians shortly after the war needs to be taken with a pinch of salt. The work of Bletchley Park was an official secret for many years. My recollection is that it was only revealed 30 or 40 years after the end of the war. So most people put too much emphasis on Malta, as it appeared that the planes and subs based there did such a great job of spotting Italian convoys carrying Rommel's supplies. When in fact Bletchley Park were reading nearly every message issued by Rommel's quartermaster. His messages were particularly easy to decrypt, because he always used the same phrase at the end of his messages.
But my recollection of the wargames were they were land-based, working out what would have happened if an amphibious landing had
already taken place. I'm sure they didn't examine whether it was actually feasible for the Wehrmacht to get across the Channel. Nor what would have happened if they had intercepted messages showing when and where landings would take place. It shouldn't be used as proof that the river barges, or any other alternative that Germany could have put together between June and October 1940, could have got several Divisions across and establish a beachhead.
I would say on your suggestion that tank factories could easily be converted to produce small landing craft for infantry, you might be right. But what about larger ships capable of carrying vehicles, and especially LSTs that can carry 10-20 tanks, trucks, artillery? I've checked the production lists of the shipyards on the River Tyne (where I live). They nearly all produced some LCTs for long periods. For instance, the Vickers-Armstrong yard which built HMS George V stopped making cruisers and destroyers 1940-41, then again 1943-44. That yard made 12 LCTs and 4 LSTs. Swan Hunter made 4 LCTs and 2 LSTs, while Hawthorn Leslie made 4 MLCs, 10 LCTs and 3 LSTs. Between them that's 9 LSTs like this:
You can't make them in a tank factory inland. Which is why the introduction of dockyards in HOI4 is so significant. Germany probably doesn't have the dockyard capacity to make these on the scale to make any amphibious assault of even a few Divisions, without stopping all sub production for 18-24 months. This is the reality - try to win the Battle of the Atlantic or try to land in the UK. Not both.
Either, in my opinion, is doomed to failure. The Allies made 1000 (one thousand) LST type ships, and several thousand cargo ships. And again I could reel off lists of the cruisers and destroyers built on the River Tyne alone, nevermind the Tees, Glasgow, Belfast, Barrow...
Germany could never hope to defeat the UK at sea. If they seriously tried to do so from 1936 they probably wouldn't win against France.
And, no, they couldn't simply Ninja 100,000 men over the Channel in secret one night. Not when the leaders liked to speak openly about their plans in their radio communications, believing that it was impossible for anyone to crack Enigma. Alternative history is interesting, but the fact is the Poles first cracked Enigma in the 1930s.