The incident happened on Cadley Causeway, Fulwood, around 7pm on Saturday, December 28 and involved an Audi Q7 and a Ford Fiesta.
Two women in the Fiesta - a mother and daughter - were taken to hospital, where they remained on Sunday afternoon.
One of the women, aged in her 80s, suffered rib fractures and a lung injury, while the second woman, aged in her 60s, suffered a wound to her head and internal bleeding.
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The collision, at the junction with Mill Lane, also caused damage to a church wall and a bus stop.
The driver of the Audi fled the scene on foot and police are asking for help identifying him.
Sgt Andy Halliwell, of the Lancashire Police TacOps team, said: "This collision has left two people in hospital with some nasty injuries and our enquiries are very much underway to establish exactly what occurred.
"We are now asking anybody with information about who the driver may have been to get in touch as soon as possible.
"Similarly, if you witnessed the collision, or saw either the Fiesta or the Audi in the moments before the collision, and have not yet been spoken to by police, please contact us."
Two crews from Preston Fire Station attended the incident and were at the scene for just over an hour.
Electricity Northwest was also in attendance to isolate the electric supply to a bus stop.
Anybody with information is asked to get in touch on 101, quoting log number 1119 of December 28.