A major renovation will certainly save money! Lots of money!
Apart from the danger of the whole thing caving in eventually - and that'll be pretty expensive! Not to mention the risk of fire.
It must cost a fortune in heating and electric bills!
I imagine the windows are hopelessly old-fashioned and draughty.
The walls are no doubt not insulated.
That means loads of heat going
out the palace every day. Good for the song-birds on cold days but not for the heating bill!
Updating the wiring will not only make the place safer, but safe lots of money as well. Imagine all the low energy-devises that the current sockets and wiring is not designed to cope with.
London as about the same latitude as Berlin and in Germany they have more solar-panels than mushrooms! So a few panels here and there on the roofs will not only safe a little extra money but send out a good signal environmental-wise as well.
A good ventilation system means windows in many places need never be opened. And that's good for security as well. -
Without the need for air-condition mind you.
Installing modern toilets and piping alone is enough to save hundreds of liters of water every single day. At the very least!
The heating system. A modern intelligent system will save loads of money every day, simply by lowering and increasing the temperature according to where people are at any given time.
Insulating the roof will with guarantee save serious money! - Alas, the birds will no longer be able to warm the feet...
In ten years BP could be the most energy-efficient palace in the world. easily reducing the costs with 50 % (I'm probably being conservative here).