Joanna Hakesley was knocked down by a stolen Mazda while walking on the pavement in Church Lane, Copthorne in West Sussex at 11.30am on Thursday.
The driver of the stolen vehicle, who was being pursued by police, fled the scene after hitting the pensioner and later abandoned the Mazda.
Ms Hakesley of Bramble Close, Copthorne, was airlifted to the Royal London Hospital where she later died.
Detective Chief Inspector Trevor Bowles, who is leading the investigation, said that it was an appalling incident and urged the public to come forward with information about the driver.
The man is described by witnesses as a white male in his 20s.
Chief Inspector Trevor Bowles said: "This is a truly appalling incident where a 70-year-old woman, who lived in the immediate area, was walking on a pavement and was struck from behind by a car deliberately evading capture.
"The driver of that car has shown no regard for the value of human life and I appeal to the communities of north Sussex and Surrey to tell me who this person is.
"The car was abandoned under the South Terminal at Gatwick Airport and we are in the early stages of detailed examination of the vehicle and of the widespread CCTV systems within the airport itself."
He added that there was no suggestion that the driver had left the country.
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