In a joint statement to mark the end of the consultation on the green paper Every child matters, the organisations said the government should place statutory duties on councils to set up strategic children's partnerships, rather than imposing structural reforms.
The group's response comes a week after the government announced it would legislate to create a post of children's services director, to assume accountability for council education departments and children's social services.
In a separate statement, one of the group's members, the Society of Local Authority Chief Executives & Senior Managers, said such directors could have limited power but unlimited accountability, causing serious recruitment problems.
The Department for Education and Skills said it would respond to the consultation early in 2004, in advance of the bill's publication.
Asylum children proposal belongs in the past
Government plans to withdraw benefits from failed asylum seekers and force their children into care belong to an earlier century, social services directors have warned.
Andrew Cozens, president of the Association of Directors of Social Services, said the proposals in the Asylum & Immigration Bill would squeeze social services at a time when the government is demanding better outcomes for looked-after children.
He said the provisions would be an initial test for the children's commissioner, whose post will be created under the Children's Bill.
Mr Cozens said: 'If put into effect, the proposal would put unacceptable pr essure on over-stretched departments.'