1942 simplified Enfield prototype

[Lee Enfield]

I am very sure this IS the rifle from RIA, note the identical light bottom of the butt stock: World War II British Enfield Bolt Action Prototype Light-Rifle Firearms Auction Lot-2626

Judging by the staining on the left side of the front band, and the damage to the right side of the forend and handguard, you are correct, it is the same gun.

the one which I examined (sorry for the crappy photos, all I had was my phone and poor light)in 2013 is a different gun - this one in Canada:
Attachment 97656
you can clearly see one of the rivets holding the barrel extension into place.
It seems they used a similar system to the Sten Mk2 barrel trunnion (riveted into place on early and British guns).
Attachment 97657[