A car and a van left the woman at the scene of the collision yesterday afternoon.
Thames Valley Police said the ‘fail to stop’ collision happened in Great Clarendon Street at the junction with Hart Street at about 3.55pm.
A small white car and a van were in collision, during which a pedestrian, a woman in her fifties was seriously injured.
The victim is still being treated in hospital this afternoon.
The drivers of both vehicles left the scene before officers arrived yesterday.
PC Lyndsey Blackaby, of the Serious Collision Investigation Unit, said: “We need to identify the vehicles involved in this collision, and the occupants of the vehicles as soon as possible.
“Anyone who knows the occupants of the vehicles, any witnesses or anyone with footage who haven’t already spoken to the police, are urged to contact the force immediately.”
Witnesses can contact TVP by calling 101, quoting investigation reference number 43210094276.