RA Service records help

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.

 

This shows the later organisation of a Troop/Battery/Regiment, from the excellent British Artillery Organisations 1939-45
More info on the 1939/40 organisation here: Organisation of a Field Regiment 1940