I found that I already had this BSA Shirley No. 4 Mk. I(T) rifle X33349 with scope 24364 listed in my No. 4 (T) research database from May 2017. It had the "TR" mark, "S51", "1945". I could not tell from the photos what other marks may or may not have been present. The most important one now would be if it has the "T" on the left flat side of the body.
It appeared to have the scope SN 24364 on the wrist but the photos then were not clear enough for me to be sure of that. It was with a No. 15 Mk. I wooden chest marked (T. LESS TELESCOPE) (correct model but likely from another rifle as was often the case and it had a canvas scope case No. 8 Mk. 2 with matching serial numbers to rifle and scope. Having the matching numbered scope case is very important to helping to verify the wartime conversion of the rifle to sniper configuration. Correct M1907 sling. Rifle was then described then as being mint. Appears to be matching numbers. Tentatively it looks like a good one and if the price is right ... it will be snapped up by someone.