Over by Easter?
By way of a precedent, Chamberlain resigned on 10th May 1940 and Churchill became Prime Minister on the same day. There was a war on at the time.
During the debate immediately preceding the change of leadership — the Norway Debate — the Conservative MP Leo Amery said this to Chamberlain: “You have sat too long here for any good you have been doing. Depart, I say, and let us have done with you.”
Amery was quoting Cromwell.
Of course, he was not suggesting that Chamberlain had broken the law in any way whatsoever.
Before he became PM, Churchill was First Lord of the Admiralty. That job no longer exists; its present-day equivalent is Secretary of State for Defence.
And that job is held by Ben Wallace MP, who was formerly a Captain in the Scots Guards.
Just saying.