Greater London is a county and region of England. London is the city within its borders. The county of GL has only ceremonial powers, with a Lord Lieutenant and a High Sheriff that represents the Queen within London. There is no government period over the regions of England anywhere, and it is mainly used for statistical purposes.
Although only the tiny City of London and the borough of Westminster has city status within GL, the whole area (all 33 districts) is governed as a single city. It has a Mayor of London and an elected assembly, including over the Cities of Westminster and London. The individual boroughs has local councils and mayors subordinate to the Mayor of London.
The UK does not incorporate local areas into cities, towns and villages, like the US does. There is an old time tradition within the UK that allows the Queen the ability to bestow city status upon individual boroughs and districts within the UK. But unlike US style incorporation, obtaining city statues in the UK comes with no real special privileges, other than the ability for the district to call itself a "city," have a ceremonial Lord Mayor instead of a regular mayor, and call its council a "City Council." No special powers comes with it.