Not familiar with these two regiments, but that's more likely to be 'C' Troop rather than 'C' Battery. Each of the two regiments would have had a 'C' Troop. A field regiment in 1939/40 would have Regimental HQ (plus the attached signals section, light aid detachment, medical officer etc.) and two batteries. Each Battery had a Battery HQ, ammunition column and three Troops, with each Troop responsible for 4 field guns (when up to full strength, at least). A B & C Troops made up the regiment's first Battery, D E & F Troops the second Battery. I think it was late 1940 when the regiments reorganised into three batteries of two troops each, instead of two batteries of three troops each. So in 1939/40 a man might belong to 'C' Troop, 225 Battery, 57th Field Regiment or 'C' Troop, 227 Battery, 113th Field Regiment.