The article only mentions the usual suspects. What about the Kents? The Gloucesters?

Edward VIII referred to Kensington Palace as The Aunt Heap, because of all the elderly relatives who holed up there. Princess Beatrice, Princess Victoria (Milford Haven), Princess Louise... later Princess Alice of Albany, maybe even the Carisbrookes... I can't imagine KP or St James's being rented out to just any one.