European walnut would have been the predominant stock wood for UK SMLEs in the WW1 period, which a lighter tight-grained walnut. While I've never had any of it tested to confirm, you also see darker walnut that COULD be black walnut from North America - which is plausible as the UK would have gotten shipments of materials from Canada, and later from the USA as war aid.
In Canada, SMLEs were held in inventory and refurbished from the WW1 era (post-Ross rifle) up to the start of LB No.4 production in 1941. During that time, Canada DEFINITELY produced local black walnut replacement SMLE stocks and you often see WW1 era C-Arrow marked SMLEs with stocks that are definitely black walnut of Canadian manufacture. You also see canadian-made replacement barrels.
After the war you see beech wood being periodically used, which carried through to WW2 era dispersal rifles and became the de-facto standard FTR stock wood during 1950's refurbs done as war stocks during the Korean War.
Indian Ishapore SMLEs, up to 1918, used imported walnut, but most of those guns were later refurbished and got luan mahogany wood.
The Austrian SMLEs were originally all walnut, but during WW1 there were wood shortages and queensland maple started to be used as a stop-gap, along with a tie plate that included pins that touched the draws to prevent hte soft wood form being battered at the draws by recoil. After WW1, both walnut and Queensland Maple was no longer used and the australians started using coachwood with re-inforced draws using copper recoil plates.