In the medieval period, the City was the full extent of London. The term London now refers to a much larger conurbation roughly corresponding to Greater London, a local government area which includes 32 London boroughs as well as the City of London, which is not one of the 32 London boroughs. The local authority for the City, the City of London Corporation, is unique in the United Kingdom, and has some unusual responsibilities for a local authority in Britain, such as being the police authority for the City. It also has responsibilities and ownerships beyond the City’s boundaries. The Corporation is headed by the Lord Mayor of the City of London, an office separate from (and much older than) the Mayor of London.

The City is today a major business and financial centre, ranking on a par with New York City as the leading centre of global finance;[2] in the 19th century, the City served as the world’s primary business centre.[3] The City has a resident population of approximately 8,000, but around 320,000 people work there, mainly in the financial services sector. The legal profession form a major component of the western side of the City, especially in the Temple and Chancery Lane areas; these are where the Inns of Court are located, of which two — Inner Temple and Middle Temple — fall within the City of London boundary.
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en.wikipedia.org/wiki/The_City_of_London