Her grandfather was taking the girl and her father to the airport so they could fly back to the family home in Newcastle upon Tyne. He parked the Mercedes Estate automatic when he realised he had forgotten something. As he got out, the car started to roll backwards, with the girl still strapped in the back. The car crashed through railings and into the water, which was about a yard from the edge of the road.
Emergency services went to the scene and divers, a dredger and people in private boats attempted to find the car. The water in the area, swollen by heavy rain, was about 12 feet deep. Eventually the car was found and the girl was removed and taken to the riverbank, where attempts at resuscitation were made.
The girl and her father are understood to have been visiting her mother's parents, who live in Shepperton, Surrey, where the accident happened.
The girl was taken to St Peter's Hospital in Chertsey, about two miles from the scene. A hospital spokeswoman said: "An emergency services doctor was at the scene when she was retrieved from the River Thames and resuscitation was attempted on the spot and also by ambulance paramedics en route to the hospital. On arrival at St Peter's shortly after 7pm, a full crash team continued resuscitation efforts but sadly she was certified dead at 7.45pm."
The names of the girl and her parents were not released. It is understood that she had two siblings.
Chief Superintendent Leigh Orwin, of Staines police, said: "This was a tragic accident. The operation to recover the girl was hampered by strong currents in the river, which is high at the moment due to heavy rain. We want to thank all those residents who helped the operation in these difficult circumstances. Our sympathy is with the family at this time."
A Surrey Ambulance Service spokeswoman said: "We were called to the towpath by someone saying there was a car in the water. Our staff found a man and a woman, who were fine apart from extreme shock. They said a car had gone in."
She added: "Boats went up and down the river looking for the car... there is a strong current and the river is high."