Two of the state's most exclusive private schools failed adequately to investigate and address allegations of sexual abuse involving students, a royal commission has found.

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.

Former King's School headmaster Tim Hawkes outside the royal commission in Sydney in 2015. Credit:Daniel Munoz

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.