The New Millgate Hotel was next door to the Manchester Sports Guild (and Pendulum) on Long Millgate according to Lisa on Man Mates . It could therefore have been this building on the right shown above - the green and while colour scheme may hint at a public house. Interestingly, the New Millgate Hotel's only mention is from a 1972 London Gazette in a list of liquidations, the registered office involved being next door to the Lass O'Gowrie on the other side of town.
New Millgate Hotel, Long Millgate. (c) London Gazette, 1972.