They said schools would be able to ignore requests for help from social services and child protection agencies because the Bill does not force them to promote children's well-being.
And they believe Government plans to make it easier for secondaries to gain foundation status and greater freedom from councils will make it harder for local authorities to ensure co-operation.
The Local Government Association has drafted an amendment to the Bill, which is likely to be supported by children's charities. It wants schools to be forced to set aside cash to support children's wellbeing and fund co-operation with other services.
The Government is expected to resist the amendment, arguing that schools will follow guidance issued by their local authority.
A Department for Education and Skills spokeswoman said it would be better if schools wished to be involved but this should not be compulsory. "It is more effective if schools want to be involved. Schools cannot provide improved educational standards without also playing a full part in addressing barriers to learning that lie outside the schools gates."
Alison King, chair of the LGA children and young people board, said: "I feel I am living in a parallel universe where one part of the DfES is saying one thing and another part is making that impossible."