I don't think the British had a snowball's chance in Hell of holding IOW if this was airborne-seaborne assaulted in July 1940. I doubt you do either.
Okay, I was going to hold my quiet but now you’ve assumed I’ll explain how it makes an ass out of both you and me.
Unlike others on this thread, I don’t/haven’t live/lived next to your proposed invasion points. I have however seen the size of roughly what the barges you’d be using and what they do in their natural environment. I have also seen how hilly something that looks flat is. The barges you are proposing to use (and this is based of the modern/relatively old but not WW2 era old barges I’ve seen) are first of all, they’re to small to carry much more than a company with light supplies, now, this wouldn’t be an issue in a river crossing of a short duration but this is a crossing of the channel under hostile control, because no matter how much you argue against it I know that the Nazis didn’t control enough of the channel to do what you are proposing (these minefields, as already pointed out, would have to stretch all the way to the English coast and would be under constant interdiction and clean up efforts by the Royal Navy/Coastal Command, and I doubt the Nazis has enough mines to keep these fields replenished). This means a barge that I’ve seen covered in tarpaulins in heavy rain would need to cross the channel whilst under enemy fire, continuous or not does not matter, it will come under fire and will have to worry about bailing the water out. This would have to be done by the soldiers, as there wouldn’t be enough sailors to bail the water out. Now imagine that 100% of your ships made it across and to the designated landing zones (and they won’t, as explained many times before). You now have tired men that will need to attack up sand/shingle at the first line of defences in many places (a.k.a. a contested landing) these tired men would be expected to get through what was in many cases bunkers or barricades, after getting across mines beaches whilst under gas attack. And then they would head to advance (at this point supposing they have ammunition, read all of the other issues with logistics such as a requirement for someone else to bring the supplies over from where the KM dumped them). At this point you would have Churchill giving a direct order to commanders to move forwards, if necessary bypassing higher commanders to expedite the commands. I wouldn’t want to be a Nazi in this situation (actually, does anyone know if the invasion force would have gas masks ?).
In response to the Isle of White, you propose that a bombing raid be carried out on Portsmouth before hand, this would be detected in advance and the fleet would be moving to react, the first wave would probably drop on the fleet at anchor, causing damage to some ships yes, but not enough to put any on the bottom for long (they could refloat most ships that would have sunk in port AFAIK), as such most elements would try leave port to escape any follow up attack, and be readily moved towards your Falschrim Jäger air convoy after people realised, heck, those aren’t bombers, even if they react to late to interdict said air convoy they are no close enough to provide accurate naval bombardment, if necessary they would be doing so aimes by spotter planes/naval attaches landed/a radio man from the local garrison’s artillery unit. It would be ad hoc as heck but still be done.
In short, your barges would need bailing, your men a rest and gas masks and your army a new paratrooper arm.