I agree with your last point. In many respects Churchill's most important victory was not against Hitler, but against Halifax who wanted to come to terms with the Germans. Halifax was no collaborationist but an old fashioned patriot who wanted to save as much of "olde England" as he could. Churchill's triumph in forcing the war cabinet to continue fightingthe war til the bitter end was one of the turning points of the war.
(See Five Days In London, May 1940 by John Lukas for a riveting description of the political battles that occurred then)