War production was altered for a number of reasons. Profit margins on low grade guns, which are the greatest portion of production, had always been very thin. So the opportunity to get government contracts with high profit margins could not be passed up. Many plants expanded and even added extra workers or extra shifts Demand did decrease slightly as men entered service, or went to work in factories and ammo for hunting became scare. Disposable income did go up as war industries paid good wages. So any gun you see made during the war was a trickle due to efforts going elsewhere.
The lasting problem for double makers after WWI, was that returning servicemen had very little interest in the old style doubles. Repeaters, both pump and semiauto were what they wanted. 3-4-5 shots not two. Wars introduce men to technology and this was true in firearms. Cars replaced horses, repeaters replaced single and doubles. Single shot rifles were replaced by bolt action repeaters, then semi automatic rifles and then fully automatic rifles in the military. Speed of fire became more of interest than having different chokes to choose from.
By the end of WWII it was all over for doubles. They were on life support and still are to this day. The problem for doubles is the flood of cheap used guns which have few people interested in them. Hard to sell a new Sterlingworth when there are 50,000 used ones. In some ways the British market had the same problem after WWI. Lots of used doubles, tens of thousands of dead young men, who never would buy doubles for three or four decades of expected life, or use a double in the family. So large numbers of doubles either sat in a closet or just got sold off as there was nobody to use them. Too much supply and almost no demand.