Are they not moving to Kensington palace?
"In the summer of 1689 William and Mary purchased Nottingham House, a Jacobean mansion built about 1605. It stood in Kensington, a village that 'esteem'd a very good Air'.
Nottingham House was owned by William's trusted Secretary of State, Daniel Finch, Earl of Nottingham, and the purchase price was £20,000."
So if it was bought by the royals and has been passed down how can it be subject to bedroom tax 