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Firstly: forgive me for not giving many sources but I haven't the time. The details should be verifiable.

Here goes: The BoE, like many big banks, is in fact a private corporation.

If you read the BoE Act of 1946, which ostensibly nationalised the bank, you'll see that share ownership still remained with whoever held shares in it previously, now with a government guarantee, neat. Yes, the government makes board appointments, but the process is not transparent and easily lobbied.

The reason the bank is so closely tied to the government (more explicitely, HM Treasury) shows how tightly interwoven parliament, The Crown and the BoE are. This has historical reasons, the BoE is the oldest institution of its kind and The Crown has had close relations to it and other corporations (British East India Company et al.) for hundreds of years. Empire as extension of corporate activity.

The Federal Reserve Bank in the US is a private corporation, as well. Since it is historically quite young, though, it is easier to verify its status visa-vis the government, check the Federal Reserve Act of 1913. The Federal Reserve is owned by a number of large banks and private interests through shareholdings.

Woodrow Wilson regretted his role in creating the Federal Reserve and its long-term consequences for the American people.

In essence: The Federal Reserve and its precursor, the BoE are privately owned, for-profit institutions. The missing 75% of your calculation are filling the establishment's pockets. Whose in particular? That's harder to figure in the UK, when you find out, let me know.

However, even the 25% going into HM treasury are not necessarily going towards revenue spent for public purposes. They are "the cut" The Crown gets for letting the BoE operate. A convenient arrangement.

So much for the profits. How does the BoE create these profits, though? Mostly by the monopoly of lending money to the government and charging interest. That interest is paid back, amongst others, by the taxes that you pay. As you can see, you are not necessarily benefitting from the process. It might be worth while finding out to see how the 25% cut is spent.

I am not sure if you are aware that governments, specifically their treasuries, can theoretically issue (and have practically issued) their own currency - and therefore wouldn't need to incur interest and, as a consequence, public debt. The process of creating money is the same for government as it is for the banks, by fiat ("out of thin air").

The "innovation" that was the BoE, was to be made MONOPOLY lender to the government, and in the process set a bad example for other countries to follow.

The BoE, the Parliament and The Crown are all located in the central part of London referred to as "The City of London". The City of London is itself a private corporation (issuing annual reports). It would be interesting to see how the BoE and The Crown interlink with that entity and the legal implications thereof.