Obviously then I am mistaken. That was just a guess off the top of my head. I've checked a few references since and, although the front end of the North-Lucas was rebuilt some years after the car was made, it appears that it was only the front wings (fenders, if you prefer) that were visibly different: the car never had a conventional radiatior and bonnet (it had a boat-like front, something similar to the Rumpler Teardrop). For some strange reason though, the rest of the body of the puzzle car bears a strong similarity to the North-Lucas.
The North-Lucas (designed by Oliver North, Chief Designer at Scammell, better known for his work in the commercial vehicle field, and financed by Ralph Lucas) was built in 1922. The body was a composite structure of aluminium, steel and wood, the wheels were carried on forged steel arms, the pivots containing the coil spring suspension and hydraulic dampers. It was rear engined (five cylinder radial) and air cooled and drive to the rear wheels was by universally jointed half shafts. Interestingly, Ferdinand Porsche patented a very similar design ten years later. Sadly the car, the only one built, was broken up in the 1940s.
As for the mystery car, I don't really know what it is, but something about that radiator suggests a Voisin C12 to me.