JP is correct, the BPC (British Purchasing Commission) wanted Remington to make No4 rifles for them, much like Savage, but Remington said they could not develop the tooling in time, and offered the 1903A1 Springfield instead.
A letter of intent to buy 500,000 rifles with an option for a further 500,000 for $5 a rifle was signed on 12 December 1940.
The introduction of Lend Lease and increased production in the UK and elsewhere reduced the British need for these rifles, and America's entry into the war killed it off because the US superceded the British contract because they needed Springfields for their own use.
The .303 Springfields never went beyond the prototype stage, but several do still exist. The rifle had several unique features. The butstock was shaped like the Lee Enfield's with the "hook" at the grip area, rather than the straight grip on the US stock. It also had receiver mounted rear sights similar to the Pattern 14/17, and the wood at the muzzle was cut back and the barrel contoured to take the No4 front sight and bayonet.
I'll have to do a little cleaning
