I note you intend to visit the Nottingham archives. perhaps check out the following
https://picturenottingham.co.uk/image-library/image-details/poster/ntgm005529/posterid/ntgm005529.html There was another hotel like the one seen here on Shakespeare Street and Lester's Temperance Hotel on Hounds Gate. A Temperance Movement Hall was designed by the renowned Nottingham Architect Watson Fothergill but never built. Watson Fothergill also built a Coffee Tavern for the Temperance Movement in Hucknall (1884).
Maybe the Coffee Tavern which may have been in Barkergate Hucknall is the establishment you are searching for.