Mrs Sherlock shouted to passers-by as she struggled
Jason King told a court how costume designer Mrs Sherlock, 42, tried to prevent a couple from stealing her handbag as they escaped in the vehicle.
She grabbed hold of the vehicle's windscreen wipers and exclaimed: "Look what is happening to me" before she lost her grasp and was dragged in front of the car.
Mark Woolley, 36, from Pentonville, and Jackie Moorhouse, 24, from West Hampstead, both north London, deny murdering Mrs Sherlock on 16 April.
Mr King said the alleged getaway car tried to reverse outside Euston station but a bus blocked it.
Mr King said: "As the car stopped, it bounced her. The car then accelerated.
"Her legs were dangling over the front. She could not hold on and she was dragged in front of the car.
"The car had stopped or it would have hit the bus. The lady on the bonnet said 'Look what is happening. Look what I have to go through.'
Bag stolen
"I heard those words. The lady on the bonnet was talking to the bus driver or that is how it looked.
"Her legs then went from one side to the front of the car. The car was stationary for a couple of seconds, maybe even less. Then it accelerated as fast as it could forward.
"Because she was hanging over the front, she fell off. The car sped off as fast as it could."
He told the jury: "The car was bouncing up and down.
"As the front wheel went over her, her body was still turning between the front and back wheel and then the back wheel went over her as well."
He said: "I was not aware of her rushing off. I was just aware of her getting up and going out the way we came in," he said.
Eventually someone came in through the back of the cafe and alerted Mr Sherlock to what had happened.
The couple were at Euston because they were travelling to Wigan, Lancashire, for her father's birthday.
The trial was adjourned until Wednesday.