I've looked for clues as to the history of the Fountain. Looking at OS maps reveals that the area where it stands on Medomsley Road was developed after about 1870.
The first relevant reference that I have found is to an Elizabeth Linsley applying for a license for a Fountain Inn in Consett. This reads as if it is the first establishment of a licensed premises, but the address is Harvey Street. I haven't found a Harvey Street in Consett.
Later in the 1870s there are two instances of applications for a full license (i.e. upgrading from a beerhouse) being turned down, and these relate to the premises in Medomsley Road. Licensees names are McGurk and Meehan. John Meehan sold up in 1876.
The next proprietor that I have found evidence for is Thomas Watson Dobson:
23 August 1878: Consett Guardian
Lanchester Brewster Sessions
[extract]
Thomas Watson Dobson was the next applicant. He was represented by Mr. H. J. Marshall, Durham, who said Dobson occupied the Fountain Hotel, in Medomsley Road, Consett. The house contained cellar, kitchen, tap-room, bar, front and back parlours, commercial room, and six bed-rooms, and there were also a three-stalled stable, coach-house, and yard. The premises belonged to Mr. Johnson, of Durham, who was willing if the bench granted a full license, to close the beerhouse in the same street known as the "Crown and Thistle." The Chairman: How far are these two houses apart?–Mr. Marshall: A hundred and fifty yards. They are both in the same street. He thought it was preferable to have one house with a full license than two beerhouses. – The applicant, in answer to a question, said the Fountain Hotel was rated at £25.
The last mention of Dobson is in August 1885 when there is an auction at the Fountain Hotel. In December 1885 it is to let.
The next licensee is Elizabeth Forster, first mention in 1886, and last mention in 1888.
That points to Michael McNally having taken over the license not long before the fire.