It is probable that no inns developed on the Market Square until the 17th century. Those on the High Street were sufficient and only when traffic increased did it become necessary to find new land. The actual market on the square was an occasional activity throughout the middle ages and there would be no commercial advantage in building there while high street lots were available. Compare, for example, Horse Fair, which has never been of commercial interest.
The was one 19th century addition, just off the Square on Silver Street. This started off as a beer shop in the 1860s and later got a proper pub licence. It was known as The Red Lion. This is now a private house.