My great uncle sailed to England in April 1940 to join the RAF.
He passed all tests and went to the OTU.
He was already flying at the time of the BoB, along with many others.
His operational debute in a Spitfire was in the autumn of 1941!
His first sortie got him involved in a 1 vs 2 sit. with 2 109's where he got out with a lot of sweat after the 109's had forgotten themselves in a prolonged dogfight low and slow and got jumped by Spitties.
No 4 hours there I'm afraid.
As for the RN, it was a seriously great force, and as the LW concluded (IMHO rightly), there would be a need for almost absolute air superiocity for operation Sealion to be possible. LW was supposed to keep the RN off.
The four stages of the BoB premium to the landings were basically :(supposed to be)
1. crippling shippings in the channel
2. dealing with the defense and logistics system of the FC/RAF (radar)
3. driving the RAF fighters out or rather destroying them. (from adlertag)
4. Softening the ports of the home fleet (that would i.e. be Portsmouth)
Stage 5 was an attempt to subdue the British through bombing, which had the extra purpose of bringing up fighters en masse.
It failed. But the LW did go about sinking shipping in the channel, and as far as I remember, shipping had to be stopped or limited in daylight. So, already in July 1940, the LW was catching up on anti-shipping.
Although they didn't do so well over Dunquerque, they had their scores in other places like the Norwegian campaign.
So, for the RN having no RAF, it would have been one nasty situation.