Part of the administration of the City of London. From Wikipedia:

The Court of Common Council, also known as the Common Council of the City of London, is formally referred to as the mayor, aldermen, and commons of the City of London in common council assembled.

Each ward may choose a number of common councilmen. A Common Councilman must be a registered voter in a City ward, own a freehold or lease land in the City, or reside in the City for the year prior to the election. He must also be over 21; a Freeman of the City; and a British, Irish, Commonwealth or EU citizen. Common Council elections are held every four years, most recently in March 2009. Common Councilmen may use the initials CC after their names.

The Common Council is the police authority for the City of London, a police area that covers the City including the Inner Temple & Middle Temple and which has its own police force – the City of London Police – separate from the Metropolitan Police, which polices the remainder of Greater London.