Senior management of The King's School in Parramatta did not report the alleged sexual assault of a student in 2013 to authorities, despite a police officer's written advice to do so.

The inaction was described by the Royal Commission into Institutional Responses to Child Sexual Abuse as "a failure by the senior management of King's".

In its report into harmful sexual behaviour of children in schools, the royal commission also found senior management at Trinity Grammar School in Summer Hill did not adequately investigate allegations that students were being "raped" in the boarding house.

The report found that senior management, including headmaster Milton Cujes???, were made aware of the allegations of sexual assault involving boarders in 2000.

School psychologist Kate Lumsdaine??? initiated her own inquiry because she was "concerned that senior staff would not investigate the allegations", the report determined.

"We are satisfied that, if Ms Lumsdaine had not interviewed the boys and reported her conclusion, there would have been no investigation of the sexual assaults that were occurring in the boarding house at Trinity in 2000," the commissioners wrote.

Trinity Grammar School reported the allegations to the relevant authorities after Mr Cujes received Ms Lumsdaine's report.

Mr Cujes, who gave evidence at the royal commission's public hearing into schools in 2016, is due to retire at the end of the year.

Trinity spokesman Richard Pegg said in a statement that the school "acknowledges with regret that its initial response to the incident of 2000 was inadequate. As the Head Master stated to the Commission, 'we could have done better, we should have done better'."

"From the day the school became fully aware of the seriousness and extent of the issue and reported it to the authorities, the school committed itself unreservedly to the review and taking of appropriate measures to ensure the safety and wellbeing of all students," Mr Pegg said.

"Since that time, the school has learnt much about how to deal with issues of abuse and bullying more effectively.

"The welfare and wellbeing of our boys are paramount and we will consider seriously for implementation all recommendations that the Commission makes in its final report."

The public hearing also examined how The King's School responded to allegations that a student indecently assaulted another boy during a school cadet camp in 2013.

In an email sent to senior staff, a senior constable advised that the alleged incident was an offence and should be reported to police.

"The commissioners are satisfied that no one at King's reported the ... camp incident to the police, despite having written advice from the police that the matter should be reported," the report found.

"This was a failure by the senior management of King's. Headmaster Dr Timothy Hawkes 'candidly' accepted that the steps that King's took were not effective in dealing with the problem in this case."

The commissioners also determined, "in 2013 a bullying culture existed at King's, both inside the boarding houses and in the school more generally".

Dr Hawkes retired from King's in June.

The inquiry into harmful sexual behaviour of children in schools also heard testimony about a Queensland high school and three primary schools.

Commissioners identified a number of systemic issues including how schools respond to allegations involving children and how allegations are reported to authorities.

Fairfax Media has also approached The King's School for comment.

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