No 10 has declined to confirm that Theresa May has full confidence in international trade minister Mark Garnier, who is the subject of an internal UK Government inquiry into sexually suggestive comments he made to his secretary.

The Prime Minister’s spokesman said he did not want to pre-empt the outcome of the inquiry being conducted by the Cabinet Office.

His comment came as Leader of the Commons Andrea Leadsom prepared to address MPs on this afternoon about allegations of inappropriate and unwanted sexual behaviour at Westminster.

Mrs May's spokesman said the PM would be present in the House to hear Ms Leadsom's statement on the issue as well as MPs' comments in the debate which will follow.

He denied claims that Mrs May was regularly updated by Conservative whips on a dossier of allegations relating to her party's MPs.

She has offered to hold talks with Speaker John Bercow on overhauling Commons disciplinary procedures amid mounting reports of abusive and inappropriate behaviour towards women.

A list of 13 MPs facing harassment allegations has been circulating at Westminster, according to The Daily Telegraph, as Number 10 again made clear any unwanted sexual behaviour was "completely unacceptable".

Meanwhile, the Guido Fawkes website claimed Tory aides had compiled a spreadsheet of 36 Conservative MPs - including 20 ministers - accused of inappropriate behaviour. The Conservatives declined to comment.

Over the weekend the Prime Minister ordered the Cabinet Office inquiry into whether Mr Garnier had breached the ministerial code over claims he asked his Commons secretary to buy sex toys and called her "sugar tits".

Asked at a regular Westminster media briefing whether the PM had full confidence in the international trade minister, the spokesman said: "There is an investigation which the Prime Minister has asked for, which is being conducted by the Cabinet Office. Obviously, I can't pre-empt that investigation."

Mrs May was also facing calls to suspend a second senior Conservative, former Cabinet minister Stephen Crabb, after he was reported to have admitted sending explicit messages to a 19-year-old woman he interviewed for a job.

In a letter to Mr Bercow, the PM said the current grievance system for dealing with complaints by MPs' staff lacked "teeth" as there was no contractual requirement for MPs to follow its procedures.

"I do not believe that this situation can be tolerated any longer. It is simply not fair on staff, many of whom are young and in their first job post-education," she wrote.

Asked about press reports of regular meetings with whips to discuss a dossier on MPs' sexual misbehaviour, Mrs May's spokesman said: "That is not true, no. There is no dossier and, therefore, the PM hasn't seen one."

The spokesman said Mrs May had responded "very quickly" to reports in the weekend's press of inappropriate behaviour at Westminster and wanted the Cabinet Office inquiry to be completed "as quickly as possible".

He declined to state whether she was aware of any further allegations relating to Conservative ministers.

"The Prime Minister is deeply concerned over recent media reports regarding the alleged mistreatment of staff by some MPs," he said.

"She has been clear that any unwanted sexual behaviour is completely unacceptable in any walk of life and she strongly believes it is important that those who work in Parliament are treated properly and fairly, as would be expected in any modern workplace.

"That's why she's written to the Speaker to ask for his support in what can be done to ensure that the reputation of Parliament isn't damaged by these allegations of impropriety.

"She has also been clear that this needs to be dealt with on a cross-party basis."

Mrs May's former communications director Katie Perrior said party whips often held information but kept it secret to use as leverage to discipline MPs.

She told BBC1's Breakfast: "The information is held by the whips because they use that to make sure that MPs know that other people within the party know exactly what they're up to and that behaviour either is not acceptable or indeed it will be used against them; 'you will vote in a certain way or we will tell your wife exactly what you've been up to,’” she explained.

Tory former minister Anna Soubry said any new grievance procedure must protect "all workers in the Palace of Westminster" not just MPs' staff.

Many MPs were "fed up to the back teeth with the level of misogynistic abuse" they face, she told BBC Radio 4's Today programme, adding: "There is a problem and we are all responsible for sorting it out.

"Theresa May, because she is a woman leader of a party, absolutely will - I'm confident of that."

Labour MP Lucy Powell compared the situation to the Hollywood abuse scandal with people desperate to advance in an industry.

She said: "When you have that mix of lots of desperate people in that environment, this sort of power abuse - because that's what it is, it's about a power inequality - can thrive."

But she said Mrs May was "too weak" to tackle the problem and in Mr Garnier's case "referring something off to the ministerial code is just not sufficient".

Labour's John Mann said he knew of four cases of "objectionable behaviour", including two where women made complaints, one to her political party and one to the parliamentary authorities.

One of the allegations "passes the criminal threshold" and one is "appalling", he claimed.

Mr Mann told LBC: "These are within the last couple of years, both of these, so we're talking of actual complaints where the woman have, in one case, been told to get lost, it's nothing to do with us, and in the other case, nothing is done and she's not even got back to with a response, which shows how badly actual complaints are treated and these are serious complaints."

The MP said he was calling for the cases, which related to two different parties but did not involve Conservatives, to be reopened.

He added: "In one case, the police were involved and then the police couldn't prosecute because the alleged assault took place abroad."

Howard Williams, Wyre Forest Conservative Association's chairman, said Mr Garnier had his support.

He said: "This happened seven years ago. I have been told the article in the Mail on Sunday is a fair account of what happened.

"I support Mark and I have nothing more to say."

Meanwhile, Dawn Butler, Labour's spokeswoman for women and equalities, has written to Mrs May welcoming the PM's letter to Mr Bercow and urged her to put party political considerations aside to put an end to "a culture that has tolerated or made light of abuse for far too long".

Ms Butler demanded to know whether Mrs May had been made aware of allegations of inappropriate behaviour by ministers and Conservative MPs before this weekend's press reports.

"All political parties have a responsibility to act thoroughly and properly where instances of unacceptable behaviour come to light, and to take appropriate action," said Ms Butler, who called for all parties to publish their complaints procedures.