Children in care were the responsibility of the whole authority, not just one of its departments, he told The TES in the wake of his one-year inquiry into the state of the care system in England and Wales.
Social services departments and care home managers come in for fierce criticism in Sir William's report, People Like Us, for failing to take seriously the educational and health needs of children in their care.
They had to act more like parents, he said. But the "scandalous" lack of education received by children in care - one-third receives none at all - was not their responsibility alone. "Education departments have a specific responsibility for children being looked after by a local authority," he said. "They must realise that these are their children, and not sideline them to social services."
The report calls for an "integrated" approach by local authorities which considers all the needs of children in care, not just the need for accommodation and protection from abuse.
As well as working more closely with residential care homes, education departments should also be offering more support to foster parents, many of whom felt they were isolated.
Children with emotional and behavioural difficulties were particularly vulnerable. Education and social services should develop joint systems for placing, financing, reviewing and supporting those children in boarding schools.
Sir William said he was encouraged by moves by many councils to develop "whole-authority" approaches, with more co-operation and collaboration between services, including the creation of cross-departmental children's committees. That was likely to benefit children in care.
The past decade has seen the virtual disappearance of homes with attached educational units - other than for children with special needs or in secure units. Sir William said it was right that children in care should be taught in the mainstream where possible.
But schools had to be encouraged not to stigmatise children in care or to exclude them, he said. Social services staff had told him their children had suffered from league tables and the new competitiveness between schools which encouraged them to exclude.