The Conservative group has refused to take up the cabinet member without portfolio role offered by the mayor. It plans instead to take on a strong opposition role.
In a letter to the mayor, Tory group leader Bob Neill says: 'To place an unelected body between yourself and the assembly can only diminish the role of the elected assembly itself. We will not be party to such a structure.'
A source close to the Greater London Assembly agreed Mr Livingstone had 'muddied the waters' between the executive and scrutiny functions of the GLA by including a total of four Labour, Liberal Democrat and Green members in his cabinet.
Former Conservative London mayor candidate Steve Norris is thought likely to take a post on Transport for London.
Who is in the cabinet
The advisory cabinet and their portfolios:
Nicky Gavron (deputy mayor)Spatial development and strategic plannin
Graham TopeHuman rights and equalities
Val ShawcrossChair of the London Fire and Emergency Planning Authority
Judith MayhewCity and business
John McDonnellConsultation and local government
George BarlowChair of the London Development Agency
Lee JasperRace relations
Diane AbbottWomen and equality
Richard StoneCommunity relations
Sean BaineLondon Voluntary Services Council
Caroline GoodingDisability rights