Today, Nick Page was quizzed by MPs on the Commons Education Select Committee. He said the authority was struggling to recruit enough social workers.
He also added that he was interested in a proposal for them to wear body cameras. He was asked repeatedly if he had considered his position.
Mr Page said: "At this stage, I'm not going to resign because of all the levels of accountability.
"I share that responsibility with the chief constable, and at the time the chief executive of the Clinical Commissioning Group, so I accept my social workers should have done better."
Arthur had been seen by social workers just two months before his death - but they concluded there were no safeguarding concerns.
Tustin was jailed for a minimum of 29 years for his murder, while Arthur's father, Thomas Hughes, was sentenced to 21 years for manslaughter.
Star was 16 months old when she was murdered by her mother's partner, Savannah Brockhill, at their home in Keighley, on 22 September 2020.
She suffered a fatal cardiac arrest after months of "neglect, cruelty and injury" at the hands of Brockhill and Star's mother, Frankie Smith.
The report revealed that what happened to Arthur and Star are not isolated incidents and their deaths reflect wider problems in child safeguarding practice, including poor information sharing between professionals and weak decision-making.
The review said it "attempts to understand how and why the public services and systems designed to protect them were not able to do so".
The review also said the child protection system must be "strengthened locally and nationally".
It also highlighted a need for a "clearer and sharper focus" on protecting children from significant harm.
The review did say that it "does not mean that the child protection system is broken" and said "indeed there is good evidence that, every day, many thousands of children are protected from harm by conscientious, committed and capable social workers, police officers, health, educational and many other professionals."
Meanwhile, Nick Page said: “The social workers that were involved directly with Arthur both of them are off work, one’s had a breakdown. And then the other one, we’re trying to get back into work at the moment.”
Caroline Johnson, a Conservative MP on the Commons’ Education Select Committee and a consultant paediatrician, asked why nobody had investigated bruises to Arthur’s back, as bruises on the back were “much more significant” than on the shins and legs, which can be as a result of play.
These were not investigated by the social worker who had seen them, with no follow-up child protection medical.
Annie Hudson, chair of the Child Safeguarding Practice Review Panel, told a committee hearing on Children’s Services and the murders of Star Hobson and Arthur Labinjo-Hughes that to say Arthur’s bruises were “ignored” rather than missed by social services was a “very fair and appropriate way of describing it”.
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