No - the point is that 'independence' is rather a non-runner as concept. The Bank has strong views - about sound money, about inflation targeting, about the efficacy or otherwise of 'printing money' (or quantitative easing). It always has had - witness the long battles between Lord Cromer, the Bank's Governor in the 1960s, and Harold Wilson, Labour Prime Minister between 1964 and 1970, and then again between 1974 and 1976. Wilson threatened to resign and to fight a 'People Versus Bankers' election rather than submit to Bank advice in 1964 and 1965. Throughout the period the Americans preferred to work with Bank people, rather than a Treasury they thought unacceptably dirigiste and 'Keynesian'.
Indeed, in my new review of Professor Forrest Capie's new history of the Bank in the 1960s and 1970s, just out in the journal Twentieth Century British History, I rather worry that this brilliant book accepts the Bank's line a little too easily:
"Capie is in danger at times of slipping into accepting the Bank’s concepts as if they are ‘right’. In particular, on page 251 he argues that Britain’s post-war balance of payment problems ‘can be expressed quite simply’. It was a matter, as Bank officials wrote at the time, of printing too much money under trade union pressure. But even though British labour costs did drift upwards in those years, very few economic historians would accept this judgement at face value. Britain in fact very rarely had a trade deficit. Much more important in causing the foreign exchange outflow that constantly undermined the pound was Britain’s official balance of payments deficit—the money she spent on pursuing her ‘East of Suez’ role in the Cold War and the maintenance of her remaining colonies and dominions".
In any case, you should be the judge - it's a long book, but a good one.