max:
If that mark on the barrel-flat were to be JA in a circle, rather than JH, then it would be the initial or Trade Mark for Josh Astbury, an action forger and filer, and parts machinist, for the trade. He operated from a workshop in the Birmingham gun quarter between the wars (and maybe earlier, perhaps from the turn of the century). I have also seen his name written as Joseph Astbury (perhaps the next or previous generation?), and also the spelling 'Asbury'. Unfortunately, not much is known about the firm since they never made-up complete guns. Nevertheless, some very high quality guns wear this mark, including my Manton-retailed John Wilkes .470!

No info on JH I'm afraid, sorry.