This is Bishop Lane Staithe in the old town it dates back to at least 1392 when it is first mentioned on some rental records, it's probably older than that. It's an narrow passage leading to the river where cargoes were unloaded. If you want to know more there's an excellent page here.
Due to an act of vandalism the usual CDPB site is not available. To view other offerings on the theme of cobbles try here.