For those not well versed in British Armoured Cars in WW II, a quick summary:
Only listing off the ones they built for themselves, that saw combat service:
Rolls Royce = 76 available in 1939. Served in the desert. Withdrawn from service in late 1941
Lanchester 6x4 = 35 built between 1929-1934. Served in the Far East early on.
Morris CS9 = 99 built in 1938. Served with the BEF in France, 1940, and in the desert early on.
Daimler Dingo = Over 6,600 built, starting in 1939. Served just about everywhere.
Guy = 101 built in 1940. Served with the BEF in France, 1940.
Humber = 5,400+ built, starting in 1940. Served just about everywhere.
Morris LRC = 2,200 built starting in 1940. Served just about everywhere. (LRC = Light Reconnaissance Car)
Daimler = 2,700 built, starting in 1941. Served just about everywhere.
AEC = 600+ built, starting in 1941.
Coventry = 220 built, starting in 1944.
Not counting the few WW I vehicles that were still around for the very early stages of WW II, and not counting the 2,200 Beaverette armoured cars that were rapidly built after Dunkirk for home defense, but did not serve abroad, this comes to just shy of 18,000 armoured cars. There are probably a few models I am missing from this list.
The ones built in the largest numbers were the Daimler Dingo (5+ models), the Humber (6+ models), and the Daimler (3+ models), which account for 14,700 of those 18,000 vehicles
The Staghound (a separate thread) was an American vehicle (T17E1), that they designed and started building, then decided to not use for themselves, but the British wanted the US to continue to build and export (so the USA did). Production started in October 1942, and by the end of the war, 3,844 had been built for other countries to use. It entered service too late in the UK to make it to the desert. It started service for the UK in Italy.