The authority fails in its legal duty to monitor its most vulnerable children, those with special educational needs.
Hackney is characterised by "a failure of political will", where squabbling councillors have let their own disagreements stand in the way of children's interests.
It has a bewildering array of policies and plans to improve schools but some of them contradict each other. In literacy there are five un-co- ordinated initiatives for raising standards.
It is an authority where "a significant number of services are in turmoil", whose organisation has been changed repeatedly and extensively.
While large numbers of pupils escape to schools outside the borough, at a cost of pounds 1.5m, only 132 come in from elsewhere.
In short, says the Office for Standards in Education report, the authority is in disarray.
Stephen Byers, the school standards minister, said: "This is an education authority which is failing to meet its statutory responsibilities. As a result children are being put at risk."
Ministers will take powers to intervene directly in local education authorities in an education bill this autumn. "I have no doubt," said Mr Byers, "that if we had the legal powers to intervene directly, those powers would have been exercised."
Instead, he invited Hackney to accept his offer of an improvement team to turn round the authority by next summer.
The inspectors' report notes that the borough is one of the poorest places in Western Europe. It has the highest proportion of pupils on free school meals in the country and, if the refugee population were to be replicated across the country, the total would be 5 million.
"But," Mr Woodhead said, "in these circumstances, disorganisation, absence of strategy, waste and inefficiency are all the more inexcusable.
"For some Hackney children, school is the one chance of an escape to a better life."
Tony Elliston, Hackney's chief executive, said the council welcomed the Ofsted report and improvement team plans. "The education offered to Hackney children is inadequate. An unacceptable number of our schools is failing."
Three of the four parties on the council have said that they will work with the team. But one group in the ruling coalition said that it might not. David Phillips, education spokesman for Hackney New Labour, a body of councillors expelled from the Labour Party, warned that they might not co-operate fully with the team unless it worked with and not against the council's management structures.