My information on this came from page 3 of the Ferris book. The P-13 was made at Enfield. The P-14, a different design, was made in the US. A British Lt Col wrote to the Chief of Ordnance about the use of the word Enfield in reference to the M1917 which was a redesign of the P-14.
The P-13 was in a hot .280 (.276 ?) caliber and was slated to replace the SMLE. When war came, it was produced (here) in .303 as a supplement to the SMLE, which proved so well suited for warfare that it was retained. The only real difference between the P-13 and the P-14 was in caliber and in the grasping grooves on the forearm.
Few P-14's seem to have served on the front lines, save in a sniper capacity.
One man above posted that Remington used the M-1917 as a basis for the Model 700-725 rifles. That is only mildly true. Those were so extensively modified for mass production at a cheap price that there isn't a lot of relationship. The safety was derived from the Enfield, and the location is distinctive.
What Remington did do was to use the M-1917 as the basis for their excellent M-30 and M-30S sporting rifles. They competed with Winchester's Models 54 and 70 during the 1920's and '30's. The revised Model 720 was never made in large quantities, as the war came. Postwar, Remington "went cheap" and designed the Model 721 series.
Also, a good many of the surplus rifles were modified into hunting rifles, sometimes with the actions modded to accept the long .375 H&H Magnum or .416 Rigby cartridges. The long action is one of the best for this, the true Magnum Mauser and Winchester M-70 being the other two of note.
The reason why the action is longer than needed for the .303 or .30/06 is that it was, remember, originally designed as the P-13 for that long .276 round, which I suspect recoiled too much to be appreciated by most soldiers. The 7mm caliber was a response to what the British encountered at the hands of the Boers with their M-95 Mausers from 1899-1902 in South Africa. They learned what it was to face accurate long range fire from magazine rifles in the hands of expert marksmen! That must have been a real revelation to a nation used to facing muskets and spears in the hands of wild tribes in their empire. It was even a shock to those who studied fighting Napoleon, when rifles were still primitive. The Baker was hardly a Mauser, and most arms then were still muskets, the old Brown Bess against whatever the French had, Charlevilles, I guess.
The P-13 can be easily distinguished from the P-14 by the grasping groves in the forearm in lieu of the more conventional long ones for the P-14 and Model 1917. They are uncommon, never having been put into mass production, as the war came in August, 1914, and existing rifles had to be used and production rapidly increased. And, reality showed that the SMLE was in fact a surpeb choice for that war. This is why the successor rifle developed during the 1930' s was based on the SMLE, the Rifle No. 4.
I honestly believe that the No. 4 is the best bolt-action battle rifle of all time. It is not the optimum for sniper use, although it fared very well in that role. But for general use, it's fine.
One of the late Jack O'Connor's .416's was made on a Model 1917 action. Too many associated Jack with just his beloved .270, but he had and used .338, .375, and .416 rifles when appropriate. Not to mention 7X57mm and .30/06... I miss his droll prose in, "Outdoor Life" and other titles.
The Eddystone- made 1917's have a rep for cracking the receivers. This was due to faulty heat treatment and did not affect those made by Remington and Winchester. Anyway, for WW II, many were re -heat treated.
Many M-1917's were sent to the Phillipines, and some sold to Latin American countries. Remington made a modified one for some of the later contracts. I think Guatemala may have ordered some. It had some Springfield features, as I recall, but I saw just one photo, many years ago.
M-1917's in really nice condition are now collectors' items.