This is an obvious desire line between the South Gates (for South Lynn, the Hardwick and part of the Friars) and The Walks (for the eastern part of the town centre and most places east and north of it), but it is currently one way for cycling, despite the available width being fairly good and a car driving contraflow during our survey visit! Of course, there are cyclists already using it illegally.
Even allowing contraflow cycling to Thomas Street would then allow Robert Street to be used to connect to the South Gates, although that is a deflection off the desire line so may not be obeyed.
Ideally, there would need to be some connection to the cycleways around the South Gates. Norfolk County Council's 2016 Cycling and Walking Action Plan claimed they had already built it, as shown on http://www.klwnbug.co.uk/2018/07/05/kings-lynns-imaginary-cycling-network/