While it is arbitrary, and not a city (in the sense that it hasn't received that status from the Queen), Greater London is absolutely a defined administrative a

While it is arbitrary, and not a city (in the sense that it hasn't received that status from the Queen), Greater London is absolutely a defined administrative area in the UK, with a governing body (the London Assembly) and a mayor (the Mayor of London -- not the Lord Mayor of London, who is the mayor of the City of London).