"H" marking on Long Branch No. 4 barrel

[Aussie48]

Hi Rangerover, If it was a Lithgow it would denote a Heavy Barrel, as it's a Longbranch my books show no H marks for any No 4 manufacturers.
I have a Shirley No 5 which has a T in the same place and I think like yours it is an Inspectors mark nothing more nothing less.

Cheers