Although I am the 'colleague' John refers to, I have spent some time digging deeper into this and the W/NH seems to be something of a mystery. The Ministry of Supply contract records for the period show that a single 500cc model W/NH was supplied to the War Office under contract C7373 in 1940 amidst a batch of 30 other 500cc machines of unspecified type.
The nomenclature 'W/NH' would suggest that this was a War Office version of the NH – known as the 'Red Hunter' in its civilian form – but this was a 350cc machine and the contract record clearly states that the W/NH was 500cc. The 500cc 'Red Hunter' was known as the VH which would suggest that the clerk in charge of recording the contract, or somone transcribing it at a later date confused the 'V' with an 'N'.
It would probably be safe to assume then that this was actually a W/VH machine.
But... it is always dangerous to be specific in the face of a mystery... does anyone know more.
Pat Ware