Even apart from the fact that after Munich and everything else it was quite rational to doubt Hitler's sincerity, there is a simpler and much more fundamental reason why neither Winston Churchill, nor any other prime minister of the United Kingdom, could have taken this offer: ever since it emerged as a coherent state, the overriding security imperative of the British government has been to prevent, at all costs, the appearance of a hegemonic power on the European continent. 

Take it from a Frenchman. ...

Churchill would never have done it. Chamberlain would never have done it. No plausible occupant of Churchill's seat would have done it, and if he had, he would have immediately been overthrown by Parliament and replaced by, well, Churchill.