Officers were following the car when it crashed just after 03:00 BST in Ashcombe Street, west London, the Met said.
The occupant of the car, a female in her 20s, died at the scene. A man is in hospital in a critical condition.
The police watchdog is carrying out an investigation into the crash.
The force said no other vehicle was involved in the collision.
A woman has died in a car crash after a police pursuit by officers investigating a drone being flown near Wandsworth prison.