Battalion support

[Grumbler]

IIRC the UK had less then a dozen tanks in the home Islands the day after Dunkirk. They were old Vickers, Miltidas MkI's and a few A-9's used for training.. I think I read this in Messinger's book 'Blitzkrieg Story'.
On War ( the U CAl Berkely web site about warfare) used to have an excellent section on Armored vehicles that included production figures. I don't think British production had been ramped up for tanks in 1940, so we are taking less then 100 per month of all types. The UK needed airplanes, mostly fighters, so that is where Lord Beaverbrook focused his production on.
Keep in mind that the home guard was armed mostly with shotguns and pitchforks. There was a story about one of the shire home guards showing up with longbows. Not sure I believe that. If it had been a Welsh unit, maybe.
If the Germans had gotteb troops ashore, they would have slaughtered the Brits. The Royal Navy wasn't going to let the Krauts get troops ashore. Any air drop would have run wild, until their ammo was gone (half a day at best) then those pitchforks would have been useful. A shotgun with ammo is a better weapon then an MG34 without ammo.
Both general staffs could count. Both general staffs knew that with a resupply route, any German invasion was doomed. That is why it didn't happen.
If you want a realistic scenario, start with the docks of one of the British costal towns. Park the Bismark in the harbor for fire support and start unloading ammo off your barges. Para drops should be on landing fields. Secure two or three landing fields and the Germans stand a very small chance of lasting a week before they die or surrender.
Here is the actual German OOB for operation sealion;

http://en.wikipedia.org/wiki/Operation_S..._of_battle

Milch wanted to start the invasion of the UK the day after Dunkirk. It might have worked then. Slip some troops into the refugees and try to grab a harbor on the sly and follow it up with airdrops.
It might have worked, then again I suspect the Royal Navy was watching out for just that sort of thing.

http://www.onwar.com/
Look at the production numbers. By 1940, England had produced less then 500 Tanks in the decade before the war. Most were light tanks and shipped to the colonies, were they awed the natives.
Tank production during 1940 was around 100 per month (average) of all types. Approximately 30% was left in France, another 30% sent to Egypt and the bulk of the rest farmed out to the colonies. That is why the Honey was received with such delight by British crews in Africa.