Looks like a British GS wagon for me - rear wheel looks right but not sure about the front. Missing the seat, associated structure and footboard amongst other parts, then again so is the IWM one
I too wondered about this vehicle when visiting the crater museum and cafe back in the late '90's. Brit GS wagons were sprung. At the time I deffinently thought it was of Brit origin; perhaps a munitions wagon from the heavy construction. The whees are British; note the drag rings on the steel wheel hubs. These items were common on English military designs.
The attached image of the Mk.X. Wagon GS courtesy of "Horse Drawn Transport of the British Army" by D.J. Smith is getting close to the mark I would think. Rod
Superb walkaround, it was the black and White photo on there that helped me with my WD Models build. Really Must remember to do more walkarounds when I see WW1 items