I wouldn't completely exclude the possibility of it being a one ton, but it seems to be a question of the axle type more than anything else.
The 1.5 tons and upwards used full floating spiral bevel or full floating hypoid types, and the 0.5 tons used semi-floating hypoid - both were numerically common as I mentioned before.
The one ton trucks, certainly 1939-47 one tons, used a semi-floating spiral bevel axle that was only used on the one tons and nothing else, and only came with six lug wheels which were disc wheels for 1939 and 1940;
and conventional drop centres from 1941-47;
The maximum gross for the one ton was 6000lbs, but the maximum gross for the lightest of several varieties of 1.5 tons was only 6700lbs (heaviest was a whopping 13,500lbs)
If the build logic was the same in 1938 as it was in 39 (open to question) the truck in the picture would likely be one of the lighter 1.5 tons - numerically much more common and more widely distributed. Note that European trucks 'built' in places like Kew were more realistically just assembled there from parts shipped over from Detroit or Windsor. Coachwork and cargo bodies were locally-sourced of course.
Oh, and the one ton trucks could and did come with dual rear wheels too - the ability to fit rear duals was presumably one of the reasons they went to drop-centre type wheels for the 1941 one ton while keeping the oddball six lug rims. The dual rear rims had bevels to lock the rear duals together in use and are amongst the rarest and most hard to obtain (read "expensive")
I had to research this for the 39 one ton I have here and the 1941 one ton I'm building next....