Nowadays known as York House, and apparently offices, this was originally built by George Tully, like a lot of the rest of the square.
According to this Heritage Statement about No. 10 by Mark Hines Architects he started building in 1723, imagining accommodation houses for Hotwells visitors, but later built this large hotel and other buildings like the Clifton Dispensary at No 12 as the spa became more popular and the square evolved into a centre of medicine. I'm a little confused by that claim as the York Hotel went up c. 1780, according to the listing, when Tully had been dead for ten years, but perhaps it means he planned it before he died.
GPS Coordinates:
51.45056, -2.62040
Location: Hotwells