Antoine was beaten to death and his sister Kenniece was suffocated
Health professionals failed to assess the risk a mentally ill mother posed to her two young children, a report into their deaths has found.
Vivian Gamor, who was schizophrenic, killed her son and daughter in Hackney, east London, in January last year.
Months earlier she was detained under the mental health act after threatening her sister with a knife.
The children's father, Jimi Ogunkoya, said the report itself was "scandalous, inaccurate and insensitive".
Gamor, 29, admitted beating Antoine, 10, and suffocating Kenniece, three, when they stayed the night at her flat.
It doesn't take a genius to work out that that there needs to be some sort of risk assessment done
She was convicted of manslaughter on the grounds of diminished responsibility at the Old Bailey in August 2007.
As a result of comments made by the judge at her trial, an internal review was ordered by the City and Hackney Local Safeguarding Children Board.
Passing sentence, Judge Peter Rook QC said: "On the face of it, this terrible tragedy could have been avoided if Gamor had not been allowed unsupervised access and the children's father's grave concerns had been given weight."
The report, published on Thursday, said the involvement of and "mismanagement" by the social services led to the children staying with their mother overnight.
It also said social services should have taken more notice of Gamor's strange behaviour towards her children, including claims she was not their real mother and that they had been swapped at birth.
Jimi Ogunkoya: 'They are always learning lessons but children are still dying'
However the report concluded that no single judgement or action had led or could have prevented the children's deaths.
Alan Wood, director of children's services at Hackney council, said the case highlighted "how unpredictable mental illness can be and the dreadful impact it can have on families".
He said all recommendations of the report had been implemented and lessons had been learned.
But Mr Ogunkoya attacked the report and said: "They're always learning lessons, but children are still dying.
"We should have been aware of the medical state of their mother - we should have been aware of this.
"It doesn't take a genius to work out that that there needs to be some sort of risk assessment done, you can't just throw the children in there and hope for the best.
"My children were living with me, they were taken out of a safe environment and... placed in to an unsafe one.
"If someone's been sectioned for violence - brandishing a knife - I don't see how that person can't pose a risk."
The family's solicitor, Bali Gill, said the report's recommendations were minimal and flawed.
She said of Mr Ogunkoya and his family: "They had hoped to finally get the answers to questions that have tormented them as to why their children were killed.
"Instead they have been served with a 14-page summary of a review that asked the wrong questions of the wrong people and for the wrong reasons and as such its minimal recommendations are flawed and it seems of little value."
The chief executive of mental health charity Sane, Marjorie Wallace, said: "(The report's) 22 recommendations are no substitute for meticulous and detailed analysis."
The Victoria Climbie Foundation, which campaigns for improvement in child protection laws, supported the family's call for a public inquiry.
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