The teenager was travelling with her mother, father and brother in the New Cross area of south London at 6.30pm on Sunday when the collision took place.
Police said a Peugeot 308 was being chased by a marked police car when it collided with the family’s Volkswagen Polo.
The girl, who was in the rear of the car, died at the scene from her injuries. Her parents and brother were taken to hospital but their injuries are not thought to be serious.
Police arrested the driver of the Peugeot, and he has been taken into custody. A female passenger was taken to hospital with minor injuries.
“An innocent family are now dealing with the tragic loss of a loved one,” said Commander Tony Eastaugh of the Metropolitan police.
“The Metropolitan police has now begun a thorough investigation into the circumstances of this terrible incident. The thoughts of our staff and officers are with the family at this time.”
Traffic police and officers from the Directorate of Professional Standards are now investigating, the force said. The Independent Police Complaints Commission has also been informed, and an investigator was at the scene assessing the circumstances of the collision.