Rather than helping to put the matter to rest, the Prime Minister's announcement of two separate, but internal inquiries, into parliamentary standards and procedures, has poured fuel on the fire.

One inquiry, to be conducted by government backbencher Celia Hammond, will work with party whips "to identify ways that standards and expectations and practices can be further improved so that professional behaviour in this place does not involve a young woman finding herself in the situation she (Ms Higgins) found herself in".

Ms Hammond would need to investigate the responses by senior ministers, including the Defence Minister, Linda Reynolds, and their staff when the alleged rape was first drawn to their attention in March 2019.

Senator Reynolds refused to answer questions in the Senate on Wednesday about when she first knew of the allegations and what she did about them, citing an ongoing Australian Federal Police investigation she did not confirm was actually under way.

Ms Higgins did not pursue a police complaint at the time of her alleged rape because she feared she would lose her job. She has since resigned and plans to reinstate the police complaint.

Ms Higgins became the focus of national attention when she spoke out about the way her complaint had been mishandled and the fact that she felt badly unsupported by her superiors.

A particular concern was that on learning of the incident Senator Reynolds summoned Ms Higgins to a formal employment meeting about the allegations in the same room the alleged rape had taken place.

Senator Reynolds, who has since apologised, said she was not aware her own office had allegedly been the scene of the alleged rape.

The second investigation, to be conducted by the deputy secretary of Prime Minister and Cabinet, Stephanie Foster, will look into the processes in dealing "with such incidents", supporting staff, and determining where the Department of Prime Minister and Cabinet should step in.

Mr Morrison's assertion on Tuesday that he had not been made aware of the rape allegation before Monday has been met with scepticism little short of derision.

Ms Higgins said two of his staffers had been involved in handling her complaint. A senior prime ministerial aide apparently checked in with her several months ago.

Former prime minister Malcolm Turnbull said it would be remarkable if Mr Morrison had not been told.

Both he and the Opposition Leader, Anthony Albanese, were supportive of Ms Higgins's call for an independent body to which political staffers could make complaints separate from party political processes.

Mr Turnbull said while the reviews commissioned by the PM would do no harm they would do very little good. Asking Ms Hammond to review the conduct of her own colleagues put her in a "very invidious position" he said.

He compared the culture in Parliament House to the corporate culture of the 1990s and said while "not all disrespect of women leads to violence against women... that is where all violence against women begins".

Given the growing number of questions about who knew what, when they knew it, and what they did, it is self-evident that it is not appropriate for a Liberal MP to take the lead on the investigation.

A demonstrably independent inquisitor needs to be appointed as a matter of urgency.