I realise I'm quoting myself, but I pondered the water situation in post number two, way back on page one of this thread. I've always assumed that the Germans would manage to get at least some soldiers across, in the first wave, and perhaps some more in the second. I don't know how they would conduct a blitzkrieg with only a handful of light tanks and some pack artillery. How many gallons of petrol does a Panzer II use in a day's fighting? How many tonnes of shells would a German howitzer fire in a day? All of that equipment has to be ferried across the Channel, and every tonne of ammunition is a tonne less water; every tonne of water is a tonne fewer artillery shells.
In 1944 we managed to get tens of thousands of well-supplied troops across the channel with tanks and total air superiority, but even with help from our American chums we failed to take Caen on the first day and bogged down thereafter. In 1940 the Germans, going the other way, would have been in a worse position. It doesn't matter if the individual fighting German circa 1940 was superhuman, there's only so far a man can dash from cover to cover without water before he collapses.
Each soldier would presumably carry his daily rations with him and perhaps a water bladder, but just that one issue alone would kill the invasion. Every well between London and Dover would have been blown up, or filled in with mustard gas. Even if we didn't implement a scorched-earth policy, I imagine that supplying tens of thousands of soldiers with water in peacetime conditions as part of an exercise is difficult. Under artillery fire it would have been even worse.
Furthermore I remember reading about a tank that we developed. The Covenanter. It was awful! The cooling system didn't work and the engine was overloaded, so it tended to overheat. We built over a thousand but didn't send any abroad because it was no good and would have been useless in the desert. Production began in 1940. I don't know how many were built by mid-1940 but I bet someone here has the figures. They wouldn't have had to drive very far to stem the German advance, and all we had to do was slow them down until they surrendered. On top of which we probably had lots of WW1 artillery pieces and armoured cars etc. Just one tank parked at a strategic river crossing would have played havoc with the German advance, and they didn't have time to spare.