Then I'm afraid you are misreading the political situation in 1940 Britain. Churchill got the PM job because he was seen as a man who would fight on. Hitler had shown he couldn't be trusted and Churchill's stance was backed in Parliament. That idea of Halifax seeking out terms never came to pass for sound reasons. And for Hitler to ever lay out a clear coherent set of terms that would be remotely acceptable to the British is all but impossible unless you change his character and warped world view.
The problem was, that unless what I read was a forgery, Churchill did laid out terms on which he would accept peace with Germany to Halifax. Those terms were considered so generous that it was considered unreasonable for Germany to offer then (and this is likely why Churchill laid out those terms knowing Hitler would never offer them). Those terms by the way, were roughly what is now, in hindsight, considered Germany would actually be willing to offer.
If they or better terms are offered, Churchil would have to deal with the fact that he promised he would accept peace under those circumstances and those circumstances have come to pass.
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