The design originated at the Royal Small Arms Factory, Enfield Lock, as the Pattern 1913 in .276 Enfield, a fat cartridge not to be confused with the U.S. .276 Pedersen. The P.13 held only five rounds, but the large diameter cartridge (base diameter .528") required a large magazine, resulting in the "pregnant" look of the P.13 and its successors.
With the onset of war, the British gave up the idea of a caliber change and modified the rifle to take the standard .303 British and the standard Lee-Enfield clips. The rifle was then called the Pattern 1914 or P.14. Since all the English arms factories were turning out Lee-Enfield (SMLE) rifles, the British contracted with Remington and Winchester to produce the P.14 in the U.S. (Eddystone was operated by Remington.)
As those contracts were winding down, the U.S. entered the war. Knowing of the vast rifle production facilities involved in making the P.14, and also knowing that the two American government rifle factories, Springfield Armory and Rock Island Arsenal, could never make enough Model 1903 rifles for the army that would be needed, the U.S. Army contracted the makers of the P.14 to modify the rifle to use the U.S. .30-'06 cartridge and the M1903 clips. The modified rifle became the U.S. Rifle, Model of 1917.
American soldiers universally called the Model of 1917 the "Enfield" because of its British origin, and to distinguish it from the Model 1903, always called "the Springfield."
Jim