The City of London differs from Greater London. There is in effect a London within London. This video explains the difference.

The Thames Riverside Strategy

A new staircase to connect London Bridge to the Riverside Walk is a core project of the Strategy. The old staircase was not clearly identifiable from street level or from the riverside, and once located, took pedestrians on a complex journey through enclosed spaces within the bridge. Even though it was regularly washed down, disinfected and brightly lit, it retained a highly unpleasant environment. The space attracted anti-social behaviour and people were mugged and assaulted on this staircase. The old staircase has now been demolished as part of the Riverside Walk Enhancement Strategy. A new staircase is now open on the Riverside Walk on the east side of London Bridge which cantilevers over the river. The staircase has an open aspect where users are overlooked from the bridge above and the walkway below. This natural surveillance helps ensure that users no longer feel uncomfortable or unsafe when walking between the bridge and the riverside and avoid the issues with the old staircase. The new staircase is constructed from high quality materials, primarily stainless steel, incorporating York stone treads and is lit by LED lighting within the handrail. The new landing for the staircase  merges into a new footbridge, which replaced the old timber footbridge, and is also paved in York stone to match surrounding paving. 

..and this one explains how the City is governed, the various organisations that make up the fabric of the City and how people are elected.

Bridge is a small ward in the City of London and is named from its closeness to London Bridge. Since boundary changes in 2003, Bridge is bounded by the River Thames to the south; Swan Lane and Gracechurch Street to the west; Fenchurch Street to the north; and Rood Lane and Lovat Lane to the east. The ward includes Fishmongers' Hall, St. Magnus-the-Martyr church, the Monument to the Great Fire of London, and the full span of London Bridge.

The City Corporation has set out a Thames Strategy to 2026 to guide the planning of the City’s riverside.  Public consultation on the Draft Thames Strategy ran from 18 March 2015 to 30 April 2015. More information can be obtained from the Corporation's web site: http://www.cityoflondon.gov.uk/services/environment-and-planning/planning/design/Pages/thames-strategy.aspx