The Bank of England

The Bank of England is the central bank of the United Kingdom and the model on which most modern central banks have been based. Established in 1694 to act as the English Government's banker, and still one of the bankers for the Government of the United Kingdom, it is the world's eighth-oldest bank. It was privately owned by stockholders from its foundation in 1694 until it was nationalised in 1946.
The Bank's headquarters have been in London's main financial district, the City of London, on Threadneedle Street, since 1734. It is sometimes known as The Old Lady of Threadneedle Street, a name taken from a satirical cartoon by James Gillray in 1797. The road junction outside is known as Bank junction.

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Why is a private bank allowed to set interest rates?