It becomes a very complicated topic. I'd certainly recommend you have a search back for posts by R Mark Davies, who posted as Jemima Fwar as I recall. He was steeped in the ins and outs of who had what and when.
In British usage the Staghounds were allotted to Armoured Car Regiments, which were indeed regarded as Corps units (one per Corps HQ). The last wartime WE for an Armd Car Regt allowed for;
RHQ – 3 armd cars (1 Daimler, 2 Staghounds)
AA Tp – 5 AA cars (nominally Staghounds with the twin .50-cal option)
Inter-comm Tp – (13 Humber scout cars)
Three Sqns, each with;
Sqn HQ – 4 armd cars + 1 scout car (3 Staghounds, 1 Daimler a/c and 1 Daimler s/c)
Hy Tp – 2 armoured cars (AEC) or 2 M3 halftracks (with 75-mm guns) and 1 Daimler s/c
Sp Tp – 3 White scout cars (each with a six strong dismount) and 1 Daimler s/c
Five Tps – each 2 Daimler a/c and 2 Daimler s/c.
Overall 767 men, 72 Armd cars (45 Daimler, 8 AEC, 5 AA and 14 Staghounds) and 65 scout cars (52 Daimler and 13 Humber).
Two standard disclaimers. First is 'some' units varied from the WE, I think you'll find numerous examples of different Tp set-ups, some of which suggest a far higher number might be required than the WE allowed for. Known changes were the disbandment of the AA Tps post Normandy, and the problems in maintaining the M3 halftracks (with 11H and 1RD) and even the AEC (1 & 2 HC + Inns of Court).
Second disclaimer, even when not asked, is that the Canadian Armd C Regts were fully equipped with Staghounds, so wherever you read Daimler armd car change it to a Staghound.
To the best of my knowledge the Recce Regts of the Inf Divs never had Staghounds on the books. They started with Humber a/c and s/c and were converting to Daimler a/c when the war in Europe ended.
Now when it gets to Armd Recce Regts, things start to become complicated…
In 11th Armd Div the Armd Recce Regt (2NY) never got Stuarts so used Daimler scout cars instead. When they were relieved by 15/19H it seems this anomaly remained so no Stuarts were deployed.
In Gds Armd Div 2WG began with Stuarts, however when they got Challengers (circa Aug44) this displaced at least a dozen Cromwells from the Armd Sqns, which were used to outfit the Recce Tp.
7th Armd Div Recce (8KRIH) had Stuarts. Offhand I can't recall if they were sawn-off or not.
I think there's an assumption that all Stuarts were subjected to the same fate, certainly Stuart Hills' memoir (By Tank into Normandy) says his Regtl Recce Tp was still gun tanks by early 1945. In Italy all the Stuarts were ordered to be jallopied. That included those in the Armd Rcce Regts which were on the originally drafted WE that allowed for two cruiser and two light tanks per Tp.
Gary