Oh, Churchill may get the boot, but Halifax would have had problems in 1940 (a member of the House of Lords acting as PM hadn't really happened since 1900... with a significant constitutional change reducing the power of the House of Lords in 1911), let alone 1942 by which time he'd been shipped off to be the Ambassador to the US, leaving Eden a much more likely candidate for the PM-ship.
Then, of cause, there's the delusion that because Halifax even considered the possibility of peace negotiations in the darkest days of 1940 he's going to roll over and deliver the Germans a peace which amounts to little less than a British surrender under all circumstances... even when they have the Americans and Russians on side; the U-Boat situation somewhat under control; no significant aerial threat to Britain and the threat of invasion long gone.