From a reference dated 1852.
This appears to refer to the Brewery Tap attached to Weston's Brewery rather than being the actual name of a house.
(Perhaps mistaken identity of the CELLAR HOUSE, previously the BLACKFRIARS TAVERN ?)

Nog was a well known product produced by Westons and it is said that the houses owned or leased by that company displayed a sign advertising the availability of `WESTONS NOG '.