Well, republicanism received a big boost after both World Wars. But with the Royal Family as popular as they are, when the UK exits the war weak and poor, the blame could have fallen on the Westminster system of government. Especially if the election of 1945 produces a hung parliament.
The people could then demand a constitution along the lines of the United States. England, Scotland, Wales, and Northern Ireland get the same rights as the American States, the Prime Minister loses his 'dictatorial' powers, and since no one wants to get rid of their beloved King, the monarch gets the executive powers that the American President has.