The British Army doesn't have artillery companies - gun, troop, battery, regiment.
In the finest traditions of the British Army, we use both company and squadron (along with platoon/troop and regiment/battalion) depending on what Corps (as in capbadge grouping rather than the field formation between Division and Army) you're discussing.
I was Royal Corps of Signals for example and we use Troop, Squadron, Regiment for our group names whereas the Corps of Royal Electrical and Mechanical Engineers use Platoon, Company and Battalion. The SAS use cavalry naming as well strangely enough, even though they're a predominantly infantry based unit.