Lots of GI - Overpaid, overhere and oversexed.
I
It's about right. Especially if you extend to 44. Need a lot for spares/ pool/ training/ transit but if you're not shipping them to Tobruk/ Rome too much then it builds up fast. A WWII British Armoured Division had around 250 to 400 ish Tanks. Now ITTL there's been some good work on making Armoured groups a bit more Panzer division like and balanced earlier on , vs 1939/40 Tank Corp with many more support vehicles,AAA, Infantry , Artillery etc so if we scale up to later in war we can probably average out better.
XXX Corp has a well documented OTL timeline and varied in strength/ divisions over it's long war. But at start of Market garden in late '44 it i had 2 Armoured Divisions -each fully ready to go, 11th and Guards. .One with 2 (11th) and one (Guards) with 3 Armoured brigades. Each Brigade has 2 Tank Regiments has about 100 (ish) operational tanks per regiment. Plus Michael Caine in a beret of course.
So 4,000 Valiant IIs and lets presume 2/3000 Victors by '44 is more than enough for 6 Armoured Divisions. My guess is in this scenario they would assign all Shermans to at least one Division and / or Canadians. Who, like WW1, kicked ass all over France. Politely. and in French when required, of course.
ITTL Brits could even operate all 6 Divisions with 3 Tank Brigades each. Trouble is I have a feeling they may be in action sooner in Iran/ USSR ITTL . The number of Tanks produced vs. number actually capable of being fielded at any one time that make a difference is vastly different. Hence my obsession with the impact of 400 + extra German tanks at Kharkov in May '42......
I suspect that by 1944 the British Army tank Division will be as follows with essentially 1 Armor Brigade of 3 battalions, 1 Recce Battalion (often same tanks), 1 armoured car battalion (often belonging to the parent Corps), 1 Mechanised (rifle) and 3 motor infantry Battalions plus supporting arms.
So (
from here) 343 tanks; 223 cruisers, 25 anti-aircraft tanks, 24 close support tanks, 63 light tanks, and 8 Observation tanks
Later on the last implementation turned the Armoured Recce Rgt into a 4th Armd Rgt and the 'Guards armoured' method was used - that is pairing an Armd Rgt with an Inf Rgt and creating effectively 4 smaller combined arms Brigades although this was not fully implemented until May 45
But the total number of AFVs for those 6 Divisions would be 2,058 tanks of all types of which 1138 are cruisers or in TTL case the latest Vickers Tank
That does not include the army tank Brigades which OTL used the Churchill - and in 1944 there was about 7 Brigades (5 NWE and 2 Italy) each with 240 tanks (including light, Observation, howitzer etc) so another 1,680 tanks
And obviously does not include efforts elsewhere such as the far east and pacific
And I am not sure how the 'light tank' will progress ITTL and they might simply become more mediums/cruisers of the same design?
That does not take into account wastage through combat and training.
A tank in late WW2 is good for as little as 6 months before requiring a rebuild at a factory or well equipped workshop and given the pace of tank development it might simply be placed into reserve training etc with the owning unit getting a more modern version or even a better tank.
For example the British built about 3000 A27 Cromwell's in the space of a year but only 1 full division (7th) was able to be equipped with them along with several Recce Regiments in other Divisions
So the required tank production effort is going to be several times what the actual front line strength is for those 6 Divisions and 7 Tank Brigades
And to put that into Context 17000 Sherman's were supplied to the British Commonwealth in WW2 from 1942 - and from memory about 6000 odd were used in the ETO
So my finger in the air is that the British army will need to produce about 9000 'Cruisers' and 3000 odd Infantry tanks to fully equip those 6 Divisions and 7 Tank Brigades for the ETO effort Jan 1944 to end of war.
