If the Luftwaffe had kept up the original policy of attacking airfields and making the RAF defend them they could have won a war of attrition?
I'm sure Churchill(who was a ruthless character in wartime) would have pursued that even to the destruction of the RAF.
I don't think this is enough, because airfields can be repaired quite easily and back then it was even easier than today.
My own decision would have been suppressing enough of the RAF. The Luftwaffe could never have attacked the north of Britain and Churchill knew it - Scapa Flow was practically out of reach without an aircraft carrier. I can't control the whole of Britain - but I can limit the options of Churchill. If I would be as ruthless as the Nazis, I could even depopulate the Isle of Wright to have a secure airbase that permits attacking England up to Leeds. And secure air superiority for some months over Southern England (until the inevitable reinforcements arrive from across the pond)
With his background at the Admiralty he would have sent the Home Fleet into the Channel as soon as invasion barges were seen. Who knows what might have happened then though I suspect a pyrrhic victory with the invasion stopped and the Home Fleet decimated.(he wanted the Captain of HMS Prince of Wales court martialled after withdrawing after the sinking of HMS Hood).
Yes - and my plan would have been going Singapur on them in that Situation. As soon as they leave port, I would be deciding where I attack them. I can choose the where and the when - when I have air superiority. Which I need for invasion anyway.
Also, I would need just one hour across the channel, but the Home fleet multiple days from a safe base when I have air superiority. They would arrive late anyway and would be better off planning a counter-invasion - open a second front when the German invasion is about to stall. Especially Wales would be a good place there, since it is hard to defend for foreign forces and the Luftwaffe would have the worst territory there to fight ground forces.
I don't think Germany has many chances of winning this battle even with a better strategy - but they could have been much more annoying. It is all a matter of how many months Germany could keep the initiative. Securing full control over Britain would be impossible, preventing reinforcements from the USA or Canada would be impossible as well. The maximum possible would have been a ceasefire, securing the occupation of France and preventing easy resupply routes to Russia. At least for some years. Since a ceasefire situation would also mean that the Commonwealth would fall apart already like it did after WW2 (because the Empire was too weak to fight the centrifugal forces), It would be a strategic victory for the full war. The UK would not be defeated. But would be no longer a global power.
Next would be the USSR....and that would be far less likely to be a success, especially since Stalin was an opponent who was way more evil than Hitler. Both had been mass murderers, but Stalin clearly outclassed Hitler.