A generation ago, cars, lorries and buses drove up and down Silver Street and Elvet Bridge. Now it is pedestrianised (with lorry access for deliveries from 6pm till 10am or 11am). Unfortunately no-one considered cycling provision.
Although Silver Street is busy at lunch times and early evening, Elvet Bridge is never so busy as to make allowing cycling unduly risky for pedestrians. Cyclists are already allowed throughout the day on Saddler Street (as are cars) and that street is much busier. So I think cycling should be allowed on Elvet Bridge all the time, in both directions.
On Silver Street, cycling ought to be allowed, again in both directions, whenever deliveries are allowed. In the mornings this would be up to 10am. While there are pedestrians using the street, there are not vast numbers at that time, but opening it to cyclists would be very useful for people travelling to work.
Obviously, other factors would need to be addressed, such as some of the one-way streets approaching Framwellgate Bridge on the west side, and turning out of Elvet Bridge at the east end.
Relaxing these restrictions would open up a lot more options for cyclists.