One phrase that cycling campaigners like to use when describing cycle-friendly, pedestrian friendly cities is permeability. A road network that is permeable doesn't have any impassable barriers (the M32, A4, etc.), or complex one-way systems that are designed to increase car traffic flow but inconvenience and endanger cyclists. A permeable road network would allow bikes to contraflow up one-way streets -ideally without having to bother spending lots of money painting in new contraflow lanes everywhere.
Does Portsmouth have this? From the limited data, not yet. One road does; with the no-entry signs replaced with No-motor-vehicle signs, and blue bike-only signs.
You'd have to test this to see if it works or if the cars get upset about it. Motorbikes and taxis will probably follow the bikes.
Elsewhere: no, one way roads, with the pedestrians encouraged to only look one way before they step out: not what you want. Again, notice the large number of bollards on the road. Parking or vehicles cutting corners must be an issue.
Again, no bike contraflow. Bikes are going to ride down there anyway, but without the signage to warn cars and pedestrians it's going to happen.
Permeability is an interesting idea. It's probable that a lot of people cycling use the odd "de-facto" contraflow on their day to day commutes. But it is not considered legitimate, and there is always the risk that our police will suddenly organise a crack-down on cyclists doing this. Formally allowing cyclists to contraflow along every one-way street would remove this risk.