My understanding is that there used to be are several rooms in the bowels of BP and Windsor that were full of wonderful old furniture. When Charles was setting up home at Highgrove and KP, he had tried to take some of the furniture and had been told off by the Queen to go and buy his own. If this story is true, and I just recollect having read it in the Press / here at TRF a while ago, then she is unlikely to be offering anything substantial to Harry. Even W&C are meant to have bought a lot of their furniture for their home at KP.
Even if it is so, the queen is old and they have to rehouse the furniture from BP because of the renovations anyway. But that doesn't sound like the queen at all. But maybe she and Charles simply disagreed about the way renovations should work - I can see this with their characts, that they might clash here - and then the queen said no in general. Just saying, IMHO, of course.