Could be England, of course. Shot taken by factory on handover? That would make more sense, though, if there were 6 (not 5) armoured cars as well as the motorbike for the 13 soldiers... Still, might be worth checking out records for the factory where they were manufactured? Can't be too hard to find out where that was if you know the make of vehicle.
Trust you've done the rounds of expert sources here: Military Archives at Cathal Brugha Barracks in Rathmines (closed at present), the curator of the permanent miltary exhibition at the National Museum in Collins Barracks, the Miltary History Society of Ireland and the centres for war studies at UCD and Trinity.
Your photo reminded me of the brilliant exhibition of WD Hogan's War of Independence and Civil War photos currently on display at the National Photographic Archive in Temple Bar. http://www.nli.ie/en/udlist/current-exhibitions.aspx?article=5df7a1ac-396b-4e71-a0dd-feb7c0b6612e
Well worth a wet afternoon, it is. There's even a few pics of armoured cars (not sure if they're the same type as in your pic) that were handed over by the British to Free State forces in 1921.