The Germans were still trying to follow the rules of war. The British suffered no such constraints. I didn't comment a week or so ago on how the British were shooting down aircraft painted white and marked with red crosses which were being used in air-sea rescue operations.
I posted an excerpt from Korda's book on that subject. The planes were picking up downed fliers who could go right back into action against Britain. Dowding reasoned that, under the Geneva Convention, that made the planes fair game - red crosses or not. On the same grounds he felt that German fighter pilots would be justified in machine gunning British fliers parachuting from destroyed aircraft over England. Dowding followed the "rules of war" as he interpreted them.
Realize that this is a decision to be prepared to use gas. Germany had the same thoughts too. Over the scope of the entire war many of the different powers at one time or another had given consideration to using chemical or biological weapons. The Germans and the Japanese certainly did (with Japan using both in China) and the Allies kept it on the table as well. In the end though no one was willing to open that can of worms. We can only speculate what would have really happened has Germany made a landing.