Hello Tomo
British CS tanks usually had their main weapon, early on 3.7in howitzer, then 3in howitzer and later, from Churchill V/Cromwell VI onwards, 95mm howitzer, in their turret, only one early Churchill Mk had the 3in howitzer in the hull and then there was Churchill 3in Gun Carrier in which turret was replaced with 3in cannon in an armoured box, but that was IIRC only a proto or limited production vehicle. British CS tanks were not infantry support vehicles, their function was to give smoke and HE support to gun tanks, which had 2pdr or 6pdr guns which had no or poor HE ammo. Later they just have more effective HE/smoke ammo than gun tanks with 75mm gun.
But British had whole class of tanks specially designed for infantry support, from Matilda I to Churchill Mk VIII, the infantry tanks. In essence heavily armoured but slowly moving mg-nets before they got US 75mm gun with good HE capacity, but lost some anti-armour power, 2pdr was excellent A/T gun up and incl 1940 and 6pdr has good A/T power during 42-43 but was inadequate against front armour of Pz V or VI.
Juha