Simon, automatic - no....but - more likely...?
Air superiority was one of the primary criteria in the original 19th July Sealion Directive. It is of course just one favourable factor that the Germans need to enjoy - but it is a biggie, and could in their mind outweight some more questionable factors. If they gained local air superiority over Eleven group's area of responsibility - then by definition they have a freer reign on the sea approaches to the Kent and Sussex
coasts.
Not totally free, of course - and as we know the RAF were to throw literally EVERYTHING that could fly at the invasion force either at sea or on landing; this was what the Operation Banquet preparations were for - for every available RAF aircraft, trainers of all types, transport aircraft etc. to attack the invasion beaches with gas munitions, both Mustard Gas and Paris Green, a period highly-toxic weedkiller/pesticide. I think it was on Feldgrau ages ago I posted up the actual operational orders for the RAF for this; Fighter Command was to give priority
over everything to escorting the Banquet Bombers to the beaches...
The problem is - this means a
second massive air battle over South-East England, and it's this that will truly attrit both air forces; the RAF of
everything, and the Luftwaffe of fighter aircraft to protect the bridgehead from this attack.
It's this air battle in the first days of any invasion that really brings the question of which air force can re-equip fastest with whatever to the fore. The "Battle Of Britain" was a tactical battle, the parameters for victory set as much by the fears of the British as the expectations of the Germans i.e. that forcing Fighter Command to withdraw north of the Thames would cede an
exploitable victory to the LW because Britain would lose her Chain Home/Chain Home Low radar-based early warning capability, thus levelling the playfield with the Luftwaffe, and forcing the rump of the RAF to fly PRE-radar defensive tactics - permanent and widespread Combat Air Patrols etc....which would be terribly wearing on aircraft and exhausting on pilots.
After an invasion, therefore - after these two air battles one after the other....the British at least STILL have the advantage of shiploads of at least partly-trained pilots coming in from abroad, from the Empire training schools - and those pilots shot down over "Free Britain" will be recovered to fly again if possible. Meanwhile, there will be RAF fighter types still in production in the shadow factories, and U.S. imports.
The Luftwaffe however doesn't have this flow of imported war materiel, and can only look forward to the regular flow from Germany's own factories or making older types operational again, like the withdrawn BF109Ds - while they can only expect replacement aircrew at the normal speed that the LW training system produced them "domestically".
Also new evidence has begun to be widely used which demonstrates the ability of RN heavy units to operate in shore bombardent of invasion shipping and related targets in 1940 with complete immunity from the LW.
Derek Robinson - Invasion 1940 attempts to argue this, and is a fresh approach. An iconoclastic little book.
I've said this too on a number of threads; Norway in 1940 and Crete in 1941 proved how vulnerable surface vessels were to concentrated aerial attack...but they
ALSO showed how surface units COULD withstand even the fiercest of air attacks until something happens to reduce their AA capability, like the AA cruisers off Crete that had to be sent back into the area of risk without repenishing their AA munitions.
One factor that is often forgotten is that by the time the RN should
WANT its capital ships to possibly enter the Channel and break the "sea bridge" between France and the invasion bridgehead...the Luftwaffe's bomber capacity will have been severely affected by its "Battle of Britain" bombing campaign against Eleven Group's airfields. It will be hard pressed to fly anti-shipping sorties AND tactical sorties in support of the Wehrmacht in Kent AND continue attacking the RAF's "home base" targets behind the British frontlines - airfields north of the Thames and west of the bridgehead, aircraft factories and other industries, longrange attacks against Northern UK ports unloading U.S. aid, etc.
As I said to Jim - have a look at John Ray for how the LW historically entered the BoB heavily attrited after May and June 1940, look at their historical losses in the BoB itself...and NOW factor in the
extra operational requirements of not only continuing that level of operations against Fighter Command behind the defenders' front line, but also flying anti-shipping operations against the RN and tactical and ground support ops in support of the Army in Kent. The Luftwaffe simply wouldn't have the strength left to do it all,
something would have to give...and ALL three requirements are vital -
Lighten up on Fighter Command and the RAF "home base", and the British ability to rebuild the RAF kicks in even
more quickly;
Cut the number of anti-shipping sorties to a minimum - and you let the RN cut the sea bridge supplying the invasion force;
Cut the number of sorties flown in support of the Wehrmacht
in Britain - and you rob the blitzkrieg in England of its vital "aerial artillery"...
For a time frontline units will be getting new British fighter stock out of the factories and reconditioned out of Beaverbook's Forward Repair Depots - but this supply will be problematic once the LW has local air superiority over Kent and Sussex and are free to range beyond that area both against Fighter Command bases north of the Thames, but also increasingly against the UK's aircraft industry. The LW is free as the "range closes" to attack training fields in the North of England and Scotland, aircraft factories in the Midlands, factory/development airfields, ATS fields and the "storage" satellite landing grounds etc. - in other words carrying the anti-Fighter Command and anti-RAF establishment campaign further and further out from the forward edge of the bridgehead. 
