British Army. In the UK, the army is not royal, though many of the regiments and corps that comprise it have been commissioned as royal by a reigning monarch. This is often confused because the British Army's sister services were all commissioned royal in their entireties, hence the Royal Navy, Royal Marines and Royal Air Force.
I do not mean to sound like a know-it-all, but I've always enjoyed working with our British cousins and find their history and peculiar distinctions quite interesting. If we go back far enough, much of it is our history, too.
Semper fi!