The P13 was designed for the new .276 brit round pre WWI. When the war started in 1914 they modified the design of the P13 and renamed it the P14. The P14 was never chambered for anything but .303.
I did not say that the P14 was originally chambered for .276 Brit, but rather than it was originally designed for .276 Brit. Even though they are chambered for different cartridges, the P13, 14, and 17 are all the same basic design.
Actually, the P14 was not even the best of it's particular family to see combat in WWI. The P17 was, IMHO, a better rifle because the rimless 30-06 cartridge precludes the possibility of rimlock which can happen in a .303 British rifle if the magazine is loaded carelessly. Also, because the magazine depth was not changed from the P14, a P17's magazine will actually hold 6 cartridges rather than the P14's five.