It looks very much like a Signals lorry. The jack legs allow it to be stabilised for the raising of an aerial. The small wheel at the rear is a cable-winder.

It looks similar in type to a this one on a Bedford Q (Wiki Commons Link), although not enough of the cab or chassis is visible on your picture to say which vehicle the crew section is mounted on.

Do you know anything about your Grandad's wartime postings that might help narrow things down in order to find more information? If he's from the Hampshire area then there's a chance he was part of 80 Wing (Signals) which specialised in airfield communications and the jamming of German location signals (knickebein).