Speaking in Parliament on Monday, Children's Secretary Ed Balls said that both he and children's minister Beverley Hughes want safeguarding board chairs to be independent.
Lord Laming, who is conducting an inquiry into serious case reviews and LSCBs, has been asked to suggest how to make the boards more independent.
Subject to Laming's recommendations, Balls said the government could change the law to bolster LSCB independence.
Michael Hart, director for children at Ofsted, said the lack of independent LSCB chairs is a concern.
He warned that Ofsted found a large number of serious case reviews are inadequate, partly because of "the lack of independence in those who chair the LSCBs".
Sharon Shoesmith, director of children's services in Haringey, the borough in which Baby P was murdered, is also the LSCB chair.
Lord Laming will deliver his recommendations to government early next year.
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Balls signals independence for safeguarding board chairs
The government has given its strongest indication yet that directors of children's services could be banned from chairing local safeguarding children's boards (LSCBs).
