A leaflet entitled Councils - top of the class for improving education argues that any attempt to manage local schools from the Department for Education & Skills would be bound to end in failure.
'Funding 25,000 schools and nine million pupils from Whitehall will not lead to an inclusive and effective education system to meet localities' and pupils' needs,' the association said.
The local management of schools system and 'years of restricting regulations' have made it impossible for councils to target funds to the schools most in need, it added.
Councils insisted that the money had gone to non-school activities within their education budgets.
This prompted Mr Clarke to issue a guarantee that all schools would receive at least a minimum increase next year.