It only appears that way because, as per usual, the British didn't call it that. They called it the 8mm BSA.

Savuti is right. The Lee Speed was definitely manufactured by BSA in 8mm BSA/.315 Lee-Enfield/8X50R. However, Taylor was speculating and got it wrong. They didn't choose it just for it's low pressure. BSA obviously picked it up because of it's close similarity (physical dimensions of the basic case and performance, and thus easy to make function in the Lee) to the cartridge that the Lee sporters had been most popularly chambered for - the outlawed .303 British.

India was the 900 pound gorilla of British sporting rifle markets in those days. None of the other markets even came close. The .303 was banned by order of the Governor-in-Council for Bombay in March, 1899, creating a very real crisis for the British gun trade. As was famously the case with the .450s some years later (ironically, there was never an order banning the .450s) a number of "replacements" for the .303 were then introduced in 1899 and 1900 - .400/.350, .400/.360, .375 2.5" Flanged, etc. The "8mm BSA" was the obvious choice for the Lee, for trade in India. The ban seems to have remained in force until independence.

You'll find the rifle on page 70 of Manton's 1926 - 1927 catalogue. "BSA .315 Lee-Enfield Magazine Sporting Rifle". The load is given as 34 grains smokeless and a 240 grain bullet for 2,030 fps. Extensive as it is, and as popular as the .303 was in the British sphere of influence at the time, the catalogue contains no .303 rifles of any kind.