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FreddieUK I don't see how the British taxpayer is going to benefit at all. According to press reports that I have seen the Crown Estate will have to reimburse Andrew around £500k, which I should imagine he will be happy to receive given that as a non working royal, he gets no money from the taxpayer.
He is being housed at Sandringham on an estate that belongs personally to the Royal family, actually the King (Sandringham & Balmoral both do) so the King is covering any shortfall there on what Andrew can pay him.
Then we come to Royal Lodge itself, Well, again press reports that I have read suggest that because of where it is located amongst other Royals the security requirements mean it can only be occupied by a Royal, and I'm not sure which Royal could live there - so I think it will stand empty and the Crown Estate will have to pay for its upkeep whereas as I understand it previously Andrew had to pay for the upkeep and that is one reason why he had a "peppercorn" rent.
One suggestion was that the Prince & Princess of Wales might have liked to move to the Royal Lodge but that ship has sailed and they are now going nearby instead.