To add a bit about the Austrian proof marks of lack thereof. It was common in the early part of the 20th century for British "best" gunmakers to purchase actions from Steyr and put their own barrels on them (they bought barreled actions too). Thus, no Austrian proof house marks would be stamped because those unbarreled actions would not have been proofed before they shipped to Britain. I have a M1900 from George Gibbs without Austrian proof marks but the same circle T mark on the barrel and action as your M1910. Your rifle's maker, James Woodward and Sons, was certainly one of the highest regarded British best gun makers of the time and they were located on St James's street (as your rifle indicates) from roughly the late 1800s until around 1937-39ish (just before WWII).
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In general, the MS M1910 was a popular rifle at the time because the take down version you have would, in many cases, been fitted in a nice, leather covered valise for travel. A lot of British officers combing the far corners of the British Empire would order, purchase and carry these rifles abroad with them on their adventures. They were considered a good "lion gun" and/or part of a battery of rifles carried on safari, perhaps along with a .256 Mannlicher and a double gun.
Unfortunately, I've seen many Mannlicher Schoenauer take down rifles of various prewar models (M1903-M1910) with the stock broken at the same spot on the wrist. I can only guess it's the thinnest part of the stock and therefore some inherent weakness there.
Have fun shooting your own wonderful piece of history... if only it could tell us where all it has been and what it has seen!