OP - is probable that you are looking at original wood soaked in linseed oil, that has been oxidizing for 70 to 140 years? I have some WWI P17 stocks here that are nearly black - I suspect is about what they were exposed to over very long time? Based on suggestion from an acquaintance, I mixed about 50% MinWax Red Mahogany stain with linseed oil - applied that to a lighter coloured hand guard - repeated applications got it much closer colour to the original stock - which was likely made for a USA P17 during WWI, but was re-used in a WWII refurbishment - but I do not know how that will go as the years go by - I am expecting the original stock to continue to darken from exposure to air - I do not know if that stained piece will "keep up" or not.
I had an acquaintance from Quebec - his Dad worked to repair oak pews in some very old churches - the carvings in some cases went rotten or were damaged - the Dad was able to replicate the carvings - but from "fresh" wood - was almost an "art" involved to stain new wood to look same as 250 year old stuff - colour, texture, finishes, centuries of use, etc.
Likely even starts with what kind of wood that the pieces are made from - not sure someone is going to make a Birch replacement piece match up to a Black Walnut original. I do not know what kinds of woods were used to make stocks for No.1 Lee Enfield - would not be surprising if various species used at one time or another. I think most rifle stocks had been made from multiple types of wood at different times - was once a concern about "does it fit / work" versus "does it match for looks".