I'm fairly sure I know exactly where the accident occurred. It is not a drive that the Duke pulled out from but a public road which crosses the A149 from the Sandringham Estate and leads to the village of Wolferton.
About twenty years ago I was travelling south from Hunstanton towards Kings Lynn on an misty, icy morning between Christmas and New Year. From the left (from the Sandringham Estate) appeared a dark blue Range Rover driver by an elderly woman wearing a headscarf. I was doing about 35mph (more than fast enough for the conditions) and I had to brake far more harshly than I would have liked. I managed to stop about ten or twelve feet from the emerging Range Rover which had hesitated and almost stopped across my path, straddling the main road. I identified the driver quite clearly as H M Queen. She waved, gave me a sort of "guilty" smile and pulled away, disappearing towards Wolferton.
I don't know what attraction that village holds for the Royal couple. Perhaps they pop down to the village to get a few groceries and the daily paper.