You'd be in the right geography...
Assuming this slightly enigmatic answer to mean no more than that this machine was British, I set about trawling through British tractor manufacturers, and found that I didn't know many.
Then, for no better reason that the cooling cowl on the engine kept reminding me of the ones used on petrol lawnmowers, I thought of Ransomes, producers of the "Rolls-Royce of lawnmowers", as they used to be called in the UK. That led to a minor breakthrough in finding their MG (market garden) range of tractors/crawlers, first produced in the 1930s. In particular the MG5, introduced in 1948 and shown below, had a striking resemblance to the puzzle machine, but I could only find pictures of it fitted with caterpillar tracks.
But after a bit more research, it seems that two new versions of the subsequent MG6 model (itself introduced in 1953) were marketed from 1956 onwards, intended for industrial use, rather than horticultural. These were designated the ITC (with tracks) and the ITW (4-wheel drive with pneumatic-tyred wheels).
So my guess is that this is the Ransomes ITW industrial tractor. These were powered by a 600-cc, air-cooled, 4-stroke, single-cylinder Sturmey-Archer engine, which propelled the earlier models to a dizzying top speed of 2.25 mph, but apparently the revised transmission of the MG6 and variants allowed speeds up to 4 mph!
