Central London is a much-used but unofficial and vaguely defined term for the most inner part of London, the capital of England. There are many definitions and each has its own notional boundary. Some are defined by clear boundaries, others less so. All definitions have in common the notion that central London is smaller than, and a subset of, Inner London.
Inner London is a defined term meaning that part of Greater London which was part of the County of London and by definition includes all of central London.
Use of Inner London in some contexts can carry negative connotations and be used only to describe those inner-city areas affected by poverty, crime, and social problems while central London carries more prestigious connotations and is used in terms of business, entertainment, tourism and desirable housing. In this context it is suggested that central London is surrounded by inner London and not part of it.