A British Remington M1903 ...

[LDVolunteer]

Hello Nick, I'm a home guard memorabilia collector. This is just a possibility. The majority of U.S. rifles sent to the U.K. and adapted for home guard use were P-17 U.S. Enfields in 30-06. The red paint was required so the home guard volunteers wouldn't try to load .303 into 30-06 chambered weapons. Most just brushed it on with little effeort for a neat job. Several thousand Springfields were also sent. The red band painted at the handguard is a fair clue. Is there anything else painted on the stock? Rarely, some home guard units would also paint .30 cal or 30-06 or cal 30-06 on the butt stock - usually in white paint.
*Just saw the pictures. I think the British crown marking is also a supporting clue. The 12/1941 date barrel throws me though. It's very late. Most of the U.S. goods showed up in 1941. Was it rebarreled in the U.K. later? I'm puzzled.
Just checked - BNP under a crown is Birmingham nitro proof.