Australian Federal Police Commissioner Reece Kershaw wrote to MPs and senators in February about the need to report crimes after former Liberal staffer Brittany Higgins went public with rape allegations.

At a Senate estimates hearing in Canberra on Tuesday, Kershaw said the letter resulted in 40 reports about sexual misconduct linked to politics.

A dozen of the reports have been marked as sensitive investigations, while a further 10 have been referred to state or territory police.

The revelation came as Labor Senator Katy Gallagher named three staffers in the prime minister’s office she said had attempted to smear the reputation of Brittany Higgins and her loved ones.

Of the 19 alleged cases of misconduct, Kershaw said the AFP had finalised its investigation into one matter, while another is the subject of ongoing inquiries.

Kershaw said seven did not relate to electorate officers, ministerial staff or official establishments.

Officers were unable to say how many were about incidents that happened within Parliament House.

Higgins says she was raped by a colleague in a minister’s office while employed as a staffer in March 2019.

After investigating the allegations, ACT police are expected to refer a brief of evidence to prosecutors within weeks.

The minister representing the prime minister at a Senate estimates hearing on Tuesday, Simon Birmingham, said he had no knowledge of an investigation into claims certain staffers backgrounded journalists against Higgins.

Scott Morrison has maintained he knows nothing about any negative backgrounding by any person in his office.

“I ask that you provide an answer as to whether Mr Carswell, Mr Leembruggen and Mr Creevey have been interviewed by Mr Kunkel,” Senator Gallagher said to Senator Birmingham, under parliamentary privilege.

“We would like an answer on that because Ms Higgins’ understanding is that they are the staff who were backgrounding against her loved ones.”

Andrew Carswell, Julian Leembruggen and Nick Creevey are all staff in Morrison’s office.

Higgins made a formal complaint to Morrison’s Chief of Staff John Kunkel in March, alleging staffers backgrounded against her or her partner as she attempted to get justice following an alleged rape.

Senator Gallagher said one journalist who came forward and forced the hand of the prime minister to launch the investigation has now withdrawn.

She questioned why Kunkel, on behalf of the prime minister, would ask the victim of an alleged rape at Parliament House in March 2019 to now demonstrate that the backgrounding did happen.

“This looks like an attempt to push back on Ms Higgins very strongly and it seems extremely unfair to me,” the Labor senator said.

Birmingham was told to get a briefing from the prime minister and come back later on Tuesday better informed.

Meanwhile, Morrison will act on the findings of a separate review of procedures on how to deal with serious incidents.

Department of Prime Minister and Cabinet deputy secretary Stephanie Foster was asked in February to look at the procedures and processes at parliament, following allegations of rape and harassment of women.

Initial advice given to the prime minister led to the establishment of a 24/7, independent, confidential and trauma-informed phone support line for all staff and parliamentarians.

The final report released on Tuesday found gaps in procedures and processes when it comes to responding to and preventing serious incidents and providing support for those impacted by them.

The report calls for the education of managers and staff on their obligations in relation to a safe and respectful workplace, and to recognise and respond appropriately to serious incidents or patterns of behaviour in the workplace.

It also seeks an independent, confidential, complaints mechanism for serious incidents.

Morrison will take the Foster report to cabinet and talk to political leaders and MPs about its implementation, telling federal parliament it is likely to be publicly released next week.

Meanwhile, Sex Discrimination Commissioner Kate Jenkins is continuing her review into deeper cultural and systemic issues that have shaped the toxic workplace over the years.