I'll try not to be rude, but this power thing and noise and the rest just sound like excuses. I suspect if the Queen was on an exchange only line at Buckingham Palace...
according to the bt checker, for the well publicised numbers and postcodes associated with the palaces (which i imagine are all direct lines to the exchange), Queenie doesn't have it so good.
Buckingham is on the whitehall exchange, with an EO line. which is currently "exploring solutions"
Balmoral Castle is on the crathie exchange, which is also an EO line. Ballater, just 7 miles down the road has FTTC HA!
Like most people on holiday, I guess she's a little cut off up there. And in London she's got to contend with the urban exchange problem, so there you go. Doesn't seem to be a money or privilege issue, I think it's just how the network is set up.