Early inquiries indicate that she was carried on the bonnet of the other car and fell from the bonnet and was in collision with a Belisha beacon. The vehicle drove away.
Police subsequently attended an address in Barnet and arrested a woman in connection with the inquiry. She was taken to a north west London police station and was subsequently bailed pending further enquiries to a date in late April.
Witnesses or anyone who has information can contact the incident room on 020 8247 7821 or Crimestoppers on 0800 555 111.
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The operation to recover the unexploded bomb near the Houses of Parliament let to disruption in central London overnight.
Southern parts of England and Wales will see sunny skies after a frosty start.
A police spokesman said the incident in the Bourke Street Mall on Friday was not related to terrorism.