Prime Minister Scott Morrison says sexual harassment allegations against former High Court justice Dyson Heydon are “very disturbing and very concerning”.

Mr Morrison says there will be a formal investigation into whether Mr Heydon’s Companion of the Order of Australia should be revoked if the “incredibly serious” allegations are upheld.

“It’s not appropriate to presuppose those processes. That’s not the way these things should be handled,” he told reporters on Tuesday.

“There should be a proper process to deal with this. There will be.

“They’re very serious allegations. They’re very concerning. And very disturbing. And on that basis, I would expect those processes to do their job.”

Labor is calling for Mr Heydon to be stripped of his honour after an independent inquiry found he sexually harassed six women.

Opposition frontbencher Bill Shorten also wants Mr Heydon to pay back the salary he earned from the royal commission into trade unions.

“Why does he get to keep his AC, and if the matter goes to court or there is further investigation, why does he get to keep all his taxpayer earnings from the royal commission?” Mr Shorten said.

“This is a time to strip him of all his recognition and get him sorted out.”

Mr Shorten was grilled at the 2014 royal commission and Mr Heydon later described him as an evasive witness.

There is no love lost between Mr Heydon and the Labor Party.

He was appointed to the High Court by John Howard and chosen to head the royal commission by Tony Abbott.

Six former associates have come forward with allegations of sexual harassment against Mr Heydon.

He denies the allegations.

“Any allegation of predatory behaviour or breaches of the law is categorically denied by our client,” Mr Heydon’s lawyers said.

“Our client says that if any conduct of his has caused offence, that result was inadvertent and unintended and he apologises for any offence caused.”

Three of the women are pursuing claims for compensation.

Chief Justice Susan Kiefel said she was “ashamed that this could have happened at the High Court of Australia”.

“The investigation found that six former court staff members who were judges’ associates were harassed by the former justice,” she said.

“The findings are of extreme concern to me, my fellow justices, our chief executive and the staff of the court.”

The independent inquiry report prepared by former inspector-general of intelligence and security Vivienne Thom has been provided to the complainants and Mr Heydon.

The Law Council of Australia praised the High Court for its handling of the matter.

“It would not have been easy for these complainants to step forward,” council president Pauline Wright said.

The inquiry report makes six recommendations on which the High Court has acted.

These include establishing a human resources policy relevant to the personal staff of justices and better induction processes for associates.

“It’s shocking … It goes to show no workplace is immune from this sort of conduct,” Mr Shorten said.

-AAP