The 97-year-old Duke was not injured in the accident, which occurred just before 3pm today (January 17). He was conscious but very shocked and shaken.
Prince Philip's auto hit another vehicle, which was carrying two women and a baby.
A source said: "The duke's routine in the coming days will continue as normal".
"I saw a auto, a black (Land) Rover, come out from a side road and it rolled and ended up on the other side of the road", Warne said.
The Palace spokeswoman added: 'Contact has been made privately with the occupants in the other auto and well-wishes exchanged'.
'This confirmed His Royal Highness had no injuries of concern.
The 28-year-old driver of the other vehicle - a Kia - was treated for cuts to her knee and the 48-year-old passenger sustained a broken wrist in the incident.
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The Duke of Edinburgh visited hospital in King's Lynn after the 97-year-old's Land Rover was struck and flipped over by a Kia.
The authority is expected to lower the maximum speed limit from 60mph to 50mph and approve installing average speed cameras on the road.
Warne said that he had the duke's blood on his hands after the collision, and that a member of royal staff gave him a cloth to clean it off.
Norfolk Police said, in accordance with policy in collisions, it breathalyzed both drivers. "The female driver of the Kia suffered cuts while the female passenger sustained an arm injury, both requiring hospital treatment", Norfolk Police said.
A Downing Street spokeswoman said: 'The prime minister has sent a private message wishing him well'. "Local police attended the scene".
Mr Warne said: "He's a very fearless man".
Philip retired from public life in 2017 after 65 years of service, during which he conducted more than 22,000 solo engagements and delivered almost 5,500 speeches.
A biography of the Duke by Basil Boothroyd, published in 1971, notes that Prince Philip has often been accused of being a less-than-steady driver. "Then I went to the black auto to help and realised it was the Duke of Edinburgh".
It's thought his 4x4 was pulling out of a driveway when it was hit by another auto. We're glad to hear he is okay! This is a red herring - age is a completely arbitrary and unreliable measure for assessing someone's ability to drive. For, as Philip's accident proved, it's not all about the elderly driver; there are countless others on the road whose lives could also be affected.
Warne, 75, had been driving with his wife along highway A149 near Sandringham, the Queen's estate, when he came upon the collision.