There's the Lanchester 6x4 from Copplestone, it wasn't produced in great numbers like the Rolls Royce, but there were still some about. The Morris CS9 Armoured car is just about 'in period' too. Some people use a range of WW1 types too.
I agree with Bezzo about the tanks, the most numerous British tank were the various marks of Vickers Lights, which were only proofed against rifle calibre weapons, so were essentially armoured cars with tracks. The Vickers Medium was also thinly armoured and didn't carry a purpose built anti-tank gun, just a short naval 3pdr (47mm) gun. Likewise the Vickers 6 ton tanks were armed with either mg or light guns, as was the Renault FT-17. The CV33 and Panzer I are other options, again not exactly likely to dominate the battlefield.
You also have the option of improvised armoured vehicles, which could range from a few mattresses tied to a lorry, to SCW type 'Flash Gordon' affairs and all points in between.