I think the SMLE could in some sense be called an American invention. James Paris Lee was born in Scotland but became an American and was American when he designed the original rifle.
Although the design went through a lot of development, one has only to look at one of the American Lee Navy rifles to see that it was basically the same gun from the very start.
BTW, the U.S. Marines used them very effectively in the Boxer conflict when the embassies of the European nations plus Japan were besieged in Peking.
Below is a cut and paste from Wikipedia:
Before World War I developed, the British Empire realized that its battle rifle, the Short Magazine Lee Enfield (SMLE) was already nearly obsolete. Compared to the German Mausers or US 1903 Springfield, the SMLE's .303 rimmed cartridge, originally a black powder cartridge, was underpowered. Additionally, the rear locking, dual lug design in the SMLE caused receiver stretching which required ever larger replacement bolt heads to be installed over the service life of the arm, and was not ideal for accuracy at shorter combat ranges. Great Britain began development of a new rifle and cartridge copying many of the features of the Mauser system. This development included a front locking, dual lug bolt action with Mauser type claw extractor as well as a new, powerful rimless cartridge of .276 caliber. However, the onset of World War I came too quickly for the UK to put it into production.
As it entered World War I, the UK had an urgent need for rifles and contracts for the new rifle were placed with arms companies in the United States. They decided to ask these companies to produce the new rifle design in the old .303 caliber for logistic commonality. The new rifle was termed the "Pattern 14." In the case of the P14 rifle, Winchester and Remington were selected. A third plant, a subsidiary of Remington, was tooled up at the Baldwin Locomotive Works in Eddystone, PA. Thus three variations of the P14 and M1917 exist, labeled "Winchester," "Remington" and "Eddystone."
When the U.S. entered the war, it had a similar extreme need for rifles. Rather than re-tool the factories to produce the standard US rifle, the M1903 Springfield, it was realised that it would be much quicker to adapt the British design for the US .30-06 cartridge, for which it was well-suited. Accordingly the factories, under the close supervision of the US Army Ordnance Department, altered the design for caliber .30-06. Winchester produced the rifle at their New Haven, Connecticut plant and Remington at their main facility at Ilion, New York and at another plant in Eddystone, Pennsylvania. The M1917 Bayonet was also produced and used on several other small arms. Winchester produced 545,511 rifles; Remington about 545,541 and Eddystone 1,181,908.