hello Runflat
having become the owner of a War Dept Riley 9 some 16 months ago and which I am in the process of totally restoring I can confirm that these are now very rare with 4 known to survive - the Bonhams car mentioned above that has been messed with as you described, although the rear body is still unoriginal as the rear body on the WD was unlike the standard tourer; and three as original as can be cars - one in S.Africa, one in Herefordshire ( the one you refer to above on the Riley Registers site) and mine which is Cheshire based.
The WD model resulted from a requirement for the War Dept for a rough terrain vehicle ( was this the first purpose built off roader?) that could do overseas expeditions as well as use as a staff car and as a result its specification uprated appropriately to include a strengthened chassis; uprated leaf springs; 21" wheels (31" diameter including tyres) - to provide increased ground clearance; a lower differential ratio of 6.75.1 ; larger long distance fuel tank of different design; all steel body of different rear design to a standard tourer which had fabric covered bodies and differing hood arrangement with a roll up rear window to provide better air flow thro' in hot climes.
The War Dept ordered 77 under contracts during 1931/32 but the factory also offered the "Army" model to the public in 1931 -still only in Army Green - although it appears not to have been popular as due to the different spec it was £310 as opposed to the standard tourers £285, and was dropped from the catalogue in '32.
The car was clearly a rough terrain success having been used to cross cross the African continent including the Sahara, taken the Jo' burgh- Capetown (961 miles) record in '32 and used in many other expeditions and rallies including a 7th place in the Monte Carlo Rally of 1934.
If you have any further info on these cars I would be pleased to know more.