Could it be the first Allard car? Sydeny Allard built a trial car arround 1935-36
Allard took a basic side-valve Ford V8 and got a crashed Ford V8 saloon and he ripped off the body and fitted it with a quickly hashed-up body, much of which came from a Bugatti previously owned by Earl Howe. The engine was moved back in the chassis to put more weight over the rear wheels and the car made its debut in the Gloucester Cup Trial - less than three weeks after building had begun.
This is not the puzzle car but it is very similar and it could have the same origin: