There is a bit of information about the park, house and the panel walls on the Bagshot Website.
https://www.bagshotvillage.org.uk/
I would actually like to find out more about the Park. But my efforts both to the Palace and Wessex's office never really got anywhere. There is some interesting information in a wedding book and in a book of Ingrid Seward.
Bagshot Park was shown to Prince Charles, Andrew and Anne as a possible place to live.
The Queen Mother wanted to buy it in the 1980's but the Queen advised against it. The QM used to visit the house even when the army was renting it. She did visit the Duke of Clarence there, but I wonder if the house was not going to be her home if the abdication hadn't happened.
It was the QM that appears to really want someone to buy the house and it was her who suggested it to Edward. It was not Edward's first choice, that was a house in London and it didn't work out.
After the Royal Army Chaplets ended their lease with the royal estates - the house stood empty and it was even looked into selling the house into the housing market. However due to its proximately to Sandhurst and several other areas of high risk sites on the area, it could not be. An American Actor even toured it in the 1990's in the hoper to purchase.
It was however judged too high risk and it was decided that they would rather have it left empty as only government and military occupancy would have been accepted at that time.