Oh my... I think I've found it. It is called Datsun Midget. It has indeed won a race in 1936 (although to me it looks a mere 10 years younger, especially for a lower class formula...). I'm nearly sure it is not the car's given name, though. On a complete picture there's some 3-digit name specified for this car, but I can't read it properly. Something like MSM Datsun or MSH Datsun...
Moreover, I suppose there may even be a mistake in this picture identification in my source. Watch the attached picture: it is made in 1936 (June 7, 1936 as far as I understood), the car is a midget and is powered by 747cc Datsun engine (like the one we speak about). And it has a number of cups near it. I believe THIS is actually a 1936 Datsun winner... I may be mistaken of course, but now I feel like that.