that the Queen knew anything about this. The enquiry was made by a Palace official, it wasn't an application as you call it, but an enquiry.
Anyone who has seen a thermal image of the palace click here will know that it leaks heat like a sieve. Lots of Public buildings in London do the same, but Buckingham Palace tales the prize.
It's not the Queen's fault, the palace is 190 years old and has 600 rooms.