There is a key desire line between Baxter's Plain and the Friars area and there's such an obvious route along Tower Street, Tower Place, Hillingdon Square and Birdcage Walk but it's currently very bitty. South of Millfleet is open to cycling, but has some poor surfaces. The crossing of Millfleet does nothing to enable cyclists to access Hillingdon Square and Tower Place is one-way southbound with no legal contraflow cycling. The northern end of Tower Place and Tower Street have no-cycling despite being used by delivery vans.
With a few traffic order changes and a little work to the Millfleet crossing, this could be a very easy and popular route.