A new junction has recently been installed in the city centre, based on similar ones pioneered in The Netherlands. The traffic lights have been removed from the junction between Jordon Well, Cox Street and Whitfriars Street and the junction has been coloured red:

Today was the first time I have been into the city centre since the junction was finished. Apparently the theory is that vehicles and pedestrians all have the same priority as each other and all vehicles need to slow down and navigate the junction with care. Similar schemes have been tried in Europe and they seem to work.