I have made several trips to England and Scotland, I would have paid to tour a royal residence but at the time it was not possible. Can you do that now?
Well personally speaking - I would avoid it like the plague.
I don’t think you can ‘get inside’ to my knowledge, all the more difficult since 9/11.
But at more ‘historic’ sites you can get tours, because they’re pretty much museums any way.
Most of the main palaces etc, I think you can visit, but it’s more on and around the grounds, rather than walking by the queens toilet if you catch my drift. But being as these sort of places are absolutely massive, you’ll still be able to make a day of it!