Looking over the beast again, the barrel appears to be made at Enfield and installed at Birmingham Repair, which was the old RSAF Sparkbrook plant which had been sold to BSA in 1906 and grabbed back by the Government in 1914.
This poor old thing has perfectly-valid markings on it from Enfield, BSA and BSA Repair (Sparkbrook) and SSA, all at the same time!
There is a discussion in Major E.G.B. Reynolds' book THE LEE-ENFIELD RIFLE regarding the awful mess which surrounded the SSA/NRF affair. They tried to buy machine-tools in England, but all which were being made were spoken for. The case was the same in the USA, which was gearing up for massive war orders for just about everything. Winchester put up a new wing of their plant to make the P-14 for England; it had to be equipped. Remington did likewise because they had orders for British, French and Russian rifles. Remington went out and bought a LOCOMOTIVE FACTORY and converted it to making rifles........ and that took an immense number of machine-tools, for the plant eventually was turning out FOUR THOUSAND rifles a day PLUS so many spare parts that they ran WW TWO on them and still had enough to sell for junk after the war....... and supply the extractors for the early Ruger 77 sporting rifles! The only parts made for the P-14/M1917 rifles after the end of 1918 were a few barrels and some EJECTORS (the only weak part in the design) late in War Two. Everything was spoken for: SSA were the guy trying to buy a drink of water in the middle of the desert. Machine tools WERE being made in Germany, but Germany wasn't selling a lot of gunmaking tools to England at that time. The only other possible source would be the Swiss...... and there was no way to ship the things, even if they had been available, which they were not.
In the end, a POOL of parts was assembled to which ALL plants could make "deposits" as available and could draw "withdrawals" as required. This resulted in everybody's parts (in theory, anyway) showing up on everybody's rifles but, in actual practice, it meant everybody's spare parts showing up on SSA's rifles. Fortunately, everybody was working to Production Gauges which were all made from the Master Gauges at Enfield, so everything FIT, which was nearly a miracle for the technology of the time.
Reynolds' book today is classed as obsolete and not deep enough or exhaustive enough..... but it was the ONLY book written on the design and development of these rifles by a MILITARY man BEFORE all the paperwork was burned in the 1960s. Yes, Reynolds wrote the book using a mass of documents which no longer exist: he is the SOLE source for some information. The book is still held in Copyright by the original Publisher, but no copies have been printed for the last 50 years. There MAY be fresh copies printed, should the market warrant (let us pray!) but, in the meantime, friend BADGER over at Milsurps dot com has an arrangement with the Publisher by which students may DOWNLOAD a pdf of this seminal book through that website ONLY. The ONLY way to get a legal download is through milsurps dot com...... and it is FREE. One thing for sure: you can't beat the price! Reynolds' book is important enough that my copy is not allowed out of my sight, period.
The times were desperate and this rifle shows it in its plethora of markings.
The so-called "Peddled Scheme" for rifles during the Great War became the pattern for the Dispersed Production rifles made during the Second War following the heavy bombing of BSA. Once they had it in operation, they were able to build MANY designs of weapons ALL OVER the British Isles, with some "factories" turning out as little as a couple of pins.... and having them show up on 2 different weapons...... and having them FIT components built in another garage or basement "factory" 200 miles away. The Dispersed Production scheme reduced the number of vulnerable production targets nearly to zero..... and the "Peddled Scheme" under which your rifle was built was the matrix of the plan. Your rifle is MUCH more important, historically, than many would think possible, for it is proof that Britain WOULD win the SECOND War, once the lessons were understood.
I have an NRF here which is all-numbers-matching, absolutely unaltered and it shoots like a dream. I will have to pull it down some time and photograph all the markings on it...... but I rather doubt it will have as many as this baby!
Hope this helps.