A View from the Cyclepath has an interesting account of how Groningen in the Netherlands came to be the world's number one cycling city.
Groningen has a population of 190,000, so it's a bit bigger than Oxford, but it's similarly a relatively flat university town. (For more on cycling in Groningen, see "At the Frontiers of Cycling: Policy Innovations in the Netherlands, Denmark, and Germany" (PDF), where it's one of the case studies.)
Could we do this here? One solution for an old city centre without space for infrastructure.
"[Groningen] is now split into four segments between which it
is impossible to drive without going out to the ring-road and
back in again."
Implementing this in Oxford would be fairly straightforward, given the radial structure already enforced by the flood meadows. Close Magdalen Bridge, Worcester St, and Thames St to cars, keeping just bus lanes and allowing access for deliveries at restricted times.
An alternative might be some kind of congestion charging scheme, but using road restrictions seems more straightforward.