I just came across this photo for sale on EBay. RR and Italians The person posting the ad says the car is Italian and that the photos were probably taken in Tripoli in 1942.
I have seen a photo of Rommel standing next to a burned out RR or Fordson armoured car in North Africa but I have no knowledge of the Axis capturing any RR-type cars intact. Does this photo really show a captured car in Italian service? Did the Axis ever use captured RR aromoured cars anywhere?
I'd suggest that what they're showing is a 1920 pattern (Mk.1a?) used by the 11th Hussars, pre-war. Note the Lewis on the turret (which would have been replaced by a Bren in 1940), and the camo pattern which the Cherrypickers used before the war.
I think by the time June 1940 rolled around, most, if not all, of the 1920 pattern cars had been replaced by Morris cars assigned to Troop and Squadron leaders. And, as mentioned above, the pre-war camoflage scheme would have been replaced with the caunter scheme.
Given that the source of the photos was a British soldier, I think the one of the Rolls was pre-war - perhaps in Palestine.
The car is probably that commanded by TSM Howarth of the 11th Hussars captured in June 1940. This was regarded as such a coup by the Italians that Howarth and his crew were at once flown to Tripoli to be presented to the Italian commander and his staff. The car was probably shipped there at a more leisurly pace.