Hence their only chance really would have been if they could keep up the momentum leading upto Dunkirk, decisively take air supremacy while we were struggling with the loss of equipment at Dunkirk - once the programs like the production of the Besal got underway and/or supplies from the US started rolling in to replace weaponry it was all uphill for any German invasion from there. [..]
That would have been a factor, but even if they had done that (which they couldn't have done*) they still wouldn't have had a chance because of the Royal Navy. Many of the RN ships were a bit dated at that time, but they had plenty of guns and it doesn't take much of a naval gun to sink an unarmoured and unarmed barge.
Not long before, Germany made opposed landings against Norway and Denmark. Those countries had a far weaker army, navy and air force than the UK, not much prepared defences
and no warning. The Germans still took massive losses doing it, despite having surprise, air superiority and naval superiority. Maybe "supremacy" would be a better word for the extreme disparity in power. Despite those things, the German navy alone lost 38 ships. Opposed landings are a bloody affair, especially when you don't even have landing craft (which hadn't been invented at that time, so nobody had them). Even if the RAF completely disappeared somehow and the UK forgot how to make planes and there wasn't a single working gun in the UK, invading Britain still wouldn't have stood a chance unless the Royal Navy disappeared as well.
Here's the known count of the
operational navy ships that would be involved, assuming that Germany put every available naval ship they had at the time into the invasion:
Kriegsmarine: 3 cruisers, 4 destroyers. And a load of unarmoured, unarmed barges full of soldiers. Some of which didn't even have an engine (they were towed). Some of which would probably have been sunk by the sea itself, because that is not a safe stretch of water by a long chalk.
British Home Fleet (i.e. ships already in the area): 5 capital ships, 1 aircraft carrier, 11 cruisers, 8 destroyers.
British Meditteranean Fleet (i.e. close enough to get there quickly): 7 capital ships, 2 aircraft carriers, 7 cruisers, 30 destroyers.
The threat seemed real coming on the heels of Germany overrunning most of Europe in weeks, but it was a convincing facade with nothing behind it. None of the German high command thought it was even vaguely close to being possible. If I recall correctly, the German naval commander said that trying it would be being like feeding meat into a mincer. I'm sure the British military would have been sickened by slaughtering so many German soldiers in a one-sided massacre, but I'm also sure they would have done it if they had to.
* The momentum was already too much and the command structure was crap. Units were all over the place, supply lines weren't there, in many cases high ranking officers making overall decisions didn't even know where some units were and conflicting orders were given due to the flaky command structure, ignorance of what was where and political infighting (particularly between commanders of different branches of the military). They'd taken a huge bite - they needed to chew it before taking another.