I believe the name "Hark unto Blue Cap," that Jean referred to in 1861 refers to a hunting hound. In the 1834 Pigot Commercial Directory the premise is listed as "Hound, or Blue Cap, Jane Greathead, Coniscliffe."
There is a Blue Cap Inn, at Sandiway. Bluecap was a foxhound owned by Mr John Smith-Barry of the Cheshire Hounds, and in 1762 took part in a famous race, at Newmarket, for a 500-guinea wager with Hugo Meynell, the Master of the Quorn Hunt.
Locally, blue cap also refers to the bluetit, the blue flame from a miners lamp with the presence of fire damp, or the mining Blue Cap Fairies who expected a fair days work for a fair days pay. There was also a Blue Cap champion Wensleydale ewe, but I believe this was around 1850, after the above 1834 date.
I believe the "Hound" in the listing is the definitive explanation, a personal opinion only!