Sgt Robert McDonald tried to get Sir Harry Djanogly, 77, out of his Jaguar XJF after pulling him over for speeding on the A40 near Acton, west London.
Sir Harry, from central London, denies dangerous driving and assaulting a police officer on 27 December 2014.
He was taking his wife to hospital when driving at 70mph in a 50mph zone.
The philanthropist, who does not deny speeding, told Isleworth Crown Court that his wife of 52 years, Lady Carol Djanogly, suffers from health problems, including emphysema, and at the time he "honestly believed that her life was in danger" and was trying to get to St John and St Elizabeth private hospital.
Sir Harry said when officers pulled up alongside him in a police van, he told them he needed to get his wife to hospital and asked them to follow him.
But when his car stopped at a red light moments later, Sgt McDonald approached the driver side window.
Sir Harry said: "He said 'get out', I said 'officer, I have explained to you before, I'm taking my wife to hospital and once I'm there...
"He said 'get out', I said 'no I'm going' and he jumped in through the window.
"I was shocked at the way he just threw himself - it is all happening in seconds."
He claimed his foot then slipped off the foot brake as the officer leant in, causing the car to move as the officer clung on.
"I know if I revved that car we would not see that man for dust - he would have, God forbid, have died," the textile manufacturer added.
Sir Harry said: "I'm regret it, I'm sorry. I'm terribly sorry this happened at all."
The millionaire, said to have assets worth Â£300m, has previously been disqualified from driving for collecting too many penalty points for speeding, the court heard.
Lady Carol told the jury she had felt unwell with "a bug" after returning to their home in Buckinghamshire from Bournemouth, and wanted to go to hospital.
Shortly before the trip she had been in intensive care for a week.
Describing Sgt McDonald's actions she said: "He put his whole body in through the window right up to his waist - it was very aggressive and a bit scary really."
The trial continues.
A millionaire has denied intending to harm a police officer who was dragged hanging out of his car along a dual carriageway in London.