Oh, the irony. ;-)

The spec as a whole -- dimensions, thread pitch, and thread direction -- were the common specs adopted by most British builders, so the British designation is appropriate in that sense.

But to delve into specifics a bit, the thread angle & profile for a British bottom bracket happens to be defined by the British Standard Cycle screw thread standard, which was originally codified by the (British) Cycle Engineers' Institute.

Well, maybe not "originally"... According to Sheldon Brown, the threading specs used by BSA (Birmingham Small Arms) were largely adopted and codified to become the British Standard Cycle spec. BSA was a British company that built motorcycles and bicycles in addition to their namesake business.