Regarding the .315 (8mm) chambering, I think the following thread will answer your questions:

http://forums.nitroexpress.com/showflat.php?Cat=0&Number=75712&an=0&page=0#Post75712

This is the thread called "8mm Lee Speed."

It was NOT the 8x57 cartridge. And John Walter seems to have it wrong in "Rifles of the World" when he lists 8x51R as a Lee Speed chambering. The evidence suggests it was the 8x50R Mannlicher cartridge. BSA literature specifies it as a 240 grain bullet, muzzle velocity of 2030 fps, muzzle energy of 2199 foot pounds. Manton (as well as BSA) advertised it as the .315. As other posters have said, it was popular because of the ban on .303 ammunition in India.

What little I can contribute here is this: the rare Lee Speeds I have seen in this caliber were marked "8 mm" on the barrel, not ".315".