I have been unable to find the significance of the "JJ" markings, but have seen them on some early British Colt autos including a 1902 military 38, see the picture and description in Sheldon's book, " A Collector's Guide to Colt's 38 Automatic Pistol' pg 118-119 but don't know what it means? Anyone venture to guess??
In addition to the 900 1903 Colt Hammer 38's, Colt had 14% of the 1902 military 38 shipped to England; about 1/3 of these for the WW l war effort in 1914-1915 including the one I own #37928, see Goddard's book " Gov't Models" pg 190 for serial #'s and shipping dates. This pistol was probably used for the Canadian Expeditionary Forces even though it was shipped to the London Armory. I also have an earlier 1902 military #14048 mfg'd in 1903. Both have the complete slide/frame/barrel british markings.
My guess is that my pistol #34448 shipped in 1914 to the dealer William R Grace and Co., NY who sold it to someone. How it made it's way to England is anyone's guess. There was a need for arms of all types during the great war, so it's easy to see how/why it ended up in England. It would be nice to think that some British officer, Canadian Officer, or British intelligence may have used it, but it may have gone to anyone. If it had been shipped to the London armory / Colt's London Agency, it would have been marked in all 3 places, frame/slide/barrel.