A coroner has condemned health and social services in Hackney for "serious and cumulative failures" in the months before a mother suffering from paranoid schizophrenia killed both her children.

Antoine and Kenniece Gamor-Ogunkoya were killed by their mother Vivian Gamor on 27 January 2007. Ten-year-old Antoine was killed after Gamor tried to strangle him and then attacked him with a claw hammer. Three-year-old Kenniece died after Gamor suffocated her with cling film before placing her body in a plastic sack.

Gamor had been suffering from paranoid delusions that her own children were stillborn and had been replaced by Antoine and Kenniece. After killing the children she contacted police, confessed to what she had done and said: "I don't care, they ain't mine."

In a narrative verdict in which she ruled that the children had been unlawfully killed by their mother, assistant deputy coroner Selena Lynch said: "The death of these children was both heartbreaking and horrifying."

She cited a "catalogue of failures on the part of several individuals in mental health and social services".

The children were being brought up by their father Jimi Ogunkoya and his parents at the time of their death. Gamor was being treated for her mental illness but social workers allowed her three unsupervised overnight visits with the children. During the third visit she killed them.

"After a short period of supervised contact there was a total failure to carry out any risk assessment," said Lynch.

Ogunkoya has been left completely heartbroken by the children's death and said he believes they would still be alive today if social workers and health staff had done their jobs properly.

"They made so many mistakes. There was a lack of communication and a lack of organisation. Had people been doing what they were supposed to have been doing I don't think my children would have died. I felt as if I was frozen out of the whole process," he said.

The coroner said: "If the risks to the children had been properly recognised and managed it is probable that the mother would not have had unsupervised overnight contact with the children on the night of 26 January 2007."

Despite her criticisms of several health and social care professionals Lynch also said others did a good job. She said that Jimi Ogunkoya was a loving father who did everything he could to help his children and Gamor.

The Guardian has seen an internal serious case review into the children's deaths. Failings identified include a decision by social workers to close the case days before Gamor killed the children saying there were no immediate child protection concerns. The review revealed that Gamor was seen 16 times by nine different professionals between October 2006 and January 2007. All said she was making good progress. Three days after her final out-patient appointment she killed her children.

"If a physical risk to the children had been identified by the mental health trust and care planning by Hackney children's and young people's service had taken account of that risk might the probability of the children being killed been significantly reduced or even avoided," the review states.

Mor Dioum director of the Victoria Climbie Foundation said: "We are concerned about the lack of transparency and accountability in this case and we want to ensure that these failures don't happen again."

Alan Wood, director of children's services at Hackney council, said: "As the coroner has identified, the social work service for children in Hackney has been transformed over the last six years. We can never be complacent about our work to keep children safe and our social workers have studied carefully the issues in this tragic case."