This post covers all the postmarks I received (2014-2019) that feature their old PPI number W7047. These postmarks were last used in 2019 (Except for The Wessexes, which used theirs until at least 2021.).
Court Post Office at Buckingham Palace
There is one main postmark that is stamped on most of the Royal Mail that is processed through the Court Post Office at Buckingham Palace. This includes letters from Buckingham Palace, Clarence House, St. James Palace, Kensington Palace, and occasionally other Royal Residences outside of London (Windsor, Birkhall, etc.)
Air Mail Stamped
Air Mail Sticker
Double Postmark
Occasionally, you will get a reply that has the typical Buckingham Palace postmark and another Postmark. This is just accidental and done when the mail is taken to the next post office on its route to you. The Mount Pleasant Mail Centre (as seen on the postmark) is London's largest sorting center and most of London's international mail is sorted through that center before heading to the Heathrow Worldwide Distribution Centre.
2nd class
Court Post Office at Windsor Castle
The other year-round Court Post Office is at Windsor Castle, which handles mail for the Royal Residences in that area (Windsor Castle, Royal Lodge, etc.). Although I have seen people get mail from Windsor Castle with the Buckingham Palace Postmark. Windsor Castle is the Queen's weekend residences. She also spends her Easter Holiday there.
The other Royal Residences don't have their own full-time Post Office. I'm not entirely sure on the details on how their mail is processed. Some of them will just have their mail taken to London and dealt with the Court Post Office at Buckingham Palace. Others have their own Franking Machine to stamp the envelopes, and then they will just deliver it to their local post office.
Sandringham House
This postmark is used for Sandringham House. The Queen spends Christmas and her Winter holiday at Sandringham House. The Royal Mail sets up a temporary post office on the Sandringham estate when the Queen is in residence.
Other
This postmark is for Bagshot Park, the Wessex's residence and office. It has in the past been used for other royal residences, which is why it is not specific to Bagshot Park.
