Thank you all for the information and comments. I will follow up the leads. Letters I am told was a farly common pub/inn name for the mid-nineteenth century.
The Northumberland Archives copies of Pigot are missing the page for Hexham.
The PhD is finished (at https://figshare.le.ac.uk/articles/thesis/A_generous_helping_The_archaeology_of_soup_kitchens_and_their_role_in_post-medieval_philanthropy_1790-1914/21187117). The way the thesis is structured there is not one single section on Hexham and I have not gone into great detail on it there.
I am in the process of transcribing several lists of these who attended the soup kitchen between about 1850 and 1900. The transcript will be available through Northumberland Archives when it is finished. There are around 1,000 individuals/heads of households, so a significant proportion of the town. At the moment I am going through the lists linking the people to census records etc which is laborious! Not everyone is easily identifiable as some names are common but I reckon I will eventually have about 80% done. My goal is to look at the demographic of those who attended soup kitchens
I am working on an article for Northumberland Archive’s blog which I will post a link to when it is finished. These lists are a really unusual survival. I have a few from one or tow other soup kitchens but these are the most extensive. I will contact your journal editor.
Thanks again Phil