There is no doubt that WD motorcycles after demob, at which point they were once again under the control of the Ministry of Supply, were allocated to other governmental organisations.

If your engine is a '51 then the magneto is driven in the opposite direction to the WD models so you'd have an anti-clock mag with a clockwise dynamo (I think the long 60w). The NOC or the VMCC could tell you where the engine was originally sent (the post-war records are more or less complete). It might give a clue.