It would require better pictures of the pipes, case and hallmarks to make a decent guess about the manufacturer, at least for me. Certainly records exist in various archives for Henry Elstone Ltd but whether they’d shed light on who they bought their pipes from a century ago is another matter.
I can tell you that Henry (1835-85) was a tea merchant turned grocer and tobacconist. With Henry’s first wife Lucy Price (1835-1868) he had two sons, George Henry Price (1858-1909) and John Alfred (1861-1920). Both were tobacconists when young, but George soon left the trade while John Alfred and later his son Alfred Claude (1901-1983) made it their life’s work.
The business was located on Market Hill from its earliest days, showing up at 9 Market Hill in the census of 1861, and then 14 Market Hill by the census of 1871. There it remained for over 110 years, continuing to appear at that location in phone books at least through 1984.
I should note that during John Alfred’s lifetime the business was named after him (“J A Elstone, tobacconist”). It wasn’t until some five years after his death that his son, Alfred Claude, renamed the business after the founder, christening it Henry Elstone Ltd in late 1924.
Expansion was far in the future during Henry’s lifetime and that of his son John Alfred. It was Alfred Claude who grew the business, adding a wholesale arm after WW2. Claude Elstone Ltd, as it was called, was established at 24 High Street where it remained over thirty years, disappearing about 1977. Other retail locations were opened too, one at 76 Howard Street (1955-1958), one at 6 Peel Street (1957-1960), and one at 25 Peel Street (1957-1961). This retrenchment suggests some degree of over-expansion, or at least declining fortunes as Alfred Claude neared retirement.
In any case based on your reading of the hallmarks the set in your photo would have been sold when Henry’s son, John Alfred was in charge of the shop.
If you’re sufficiently interested you can readily find various images of the shop at 14 Market Hill online.