Judging off the pics you have posted:
1. Gun does not look like anything that Churchills would've sold or made.
2. The barrels look to be way off the face. Look at the gaps around the dolls head, usually indicative of the barrels moving forward.
3. Churchill actually made very few guns, and as far as I know, they never made guns for the trade. Most all of the Churchill guns were made in the trade. A few very high end guns were made at their workshop at the shooting grounds. The actual Churchill factory was more or less a place that repairs took place.
If it's a Churchill, it'll have Churchill on it. The company was big into their "brand" and loved to advertise and get their name out there anyway they could. They weren't known for being cryptic.
Whatever your gun is, it's interesting and was made with quality parts.