Those 1953 SMLE FTR rifles are an interesting niche. I've had maybe a dozen over the years, everything from WW1 era stuff, even some peddle schemes, to rifles like you Dispersal rifle. The receiver could be anything, but the overhauls are clearly done at BSA with BSA barrels and a mix of refurbished parts.
These were made up at FTR, Suncorite painted and fitted with new or refurbished furniture, and put into war reserve near the end of the Korean War. When they were surplussed in North America, they were all refurb-like-new. These were only intended to ever be issued if they ran out of No.4's in a new global war that never came (thankfully).
Neat rifles, and often they are great shooters with as-new bores.