Not an exhaustive list but might start you off on some interesting lines of research
11th Hussars had 1924 pattern cars until '41 - they gave up the last of their 1920 pattern cars in about 1938.
No. 1 Armoured Car Company RAF had a few surviving 1920 pattern cars initially in Iraq and later in the Western Desert. One of these is the subject of a famous photo of a wrecked car being instected by Gen. Rommel
No. 2 ACC had 1920 pattern Rolls bodies mounted on a Fordson chassis. Some of these cars remained in service until 1944.
An RAF Armoured Car Section used 1920 pattern cars in Aden until about 1943. I suspect these would have been Fordson cars especially in later years as the original Ghost chassis must have been worn out
Note sure how many survived and for how long in home based roles.