I found this No1 MkIII at an online auction in Oregon, where fortunately for me it suffered from a poor description and similarly poor photography, so it came home for the price of a No1 MkIII*, ca 2014. I was excited when I drove down to pick it up and found that not only was it a 1928 BSA but, as hinted at by the stock disc, it was indeed Iraqi property marked on the knox form, action and buttstock wood.
A very scarce year and an equally scarce Iraqi property marked SMLE. Assuming it was delivered close to the year of production indicated on the socket and the barrel, it was used in the era of the Kingdom of Iraq Under British Administration, and thereafter. It has no import marks, so it did not come into the US, like so many other Iraqi stamped SMLEs, via the Federal Ordnance imports of Israeli captured weapons (like my Iraqi marked K98k). https://sks-files.com/index.php?topic=1894.msg21925#msg21925
It's odd that the proof marks and view marks are all from RSAF Enfield with no script Bs indicative of proof at BSA. The first L block marked BSAs appeared in 1928, at least I haven't found an earlier year yet, and the last in this block of 100,000 was completed early in WWII, 1941. Hence, there was very little production in the 1920s and 1930s.
Thanks for looking!