Children's secretary Ed Balls responded to the report by sacking the director of children's services Sharon Shoesmith.
Two senior councillors - leader George Meehan and director of children's services Liz Santry - resigned.
Margaret Eaton, chair of the Local Government Association, said: "Councillors and council staff will agree with the report that safeguarding children in Haringey has gone terribly wrong.
" The report will give children’s services in the borough the chance for a fresh start, and town hall leaders will work closely with the new team to give the necessary support to help the council get on with this difficult work."
She added that the toddler's death in 2007 appeared to show Haringey was an exceptional case and that councils will be working with health services and the police to make sure lessons are learned.
“It is time to move away from a stop-go approach to child protection and make sure there is instead a consistent and effective programme of work on this important issue.
"Britain has one of the best records in the world when it comes to keeping children safe from harm and only four nations have fewer child murders each year, but even one death is too many and we must always aim to reduce numbers further.
“The emphasis now must be on how we nurture and protect vulnerable children, getting involved early with troubled families and helping them in practical ways, such as by providing parenting advice and support with mental health issues or drug dependency.”
Other LGCplus reports on Baby P