Firstly, I didn't even mention what the value might be. I simply pointed out that the "independent organisation" would not really be independent. Which means it won't protect anyone's privacy. Which undermines the entire point of having it. Therefore it has no value.
Secondly, it is the central bank that sets the interest rate. In the UK that is the Bank of England. Secondly the government sets their mandate. They have a mandate of keeping the inflation at 2%. One of the mechanisms they to control inflation is the interest rate.
https://www.bankofengland.co.uk/monetary-policy/inflation
Moreover the "Chair of the Court of Directors" (the Chairman) of the Bank of England is appointed by the Crown (the King) at the advice of the Prime Minister and the Chancellor of the Exchequer.
The government both sets the mandate and effectively selects the Chairman. So while they don't directly set the interest rate, they do set the mandate and who runs the Central Bank.
BTW the Bank of England is failing to keep the inflation rate at 2% (and for some time) as it is currently 3.4%. So we can see how well that is going.
