Original: The Lord Mayors and Provosts of Belfast, Cardiff, Edinburgh, Glasgow, City of London and York all have the further right to be styled "The Right Honourable the Lord Mayor" (or Provost), although they are not members of the Privy Council as this style usually indicates.
Simplified: The Lord Mayors or Lords Provost of Belfast, Cardiff, Edinburgh, Glasgow, City of London, and York are called "The Right Honourable the Lord Mayor" (or Provost).