According to The Sun, when Sir Michael and Ms Leadsom were on committee together, she once complained of cold hands to which Sir Michael is said to have replied: “I know where you can put them to warm them up.”
Leader of the House Ms Leadsom passed a dossier of claims to No 10 after Sir Michael was allowed to escape censure for an incident in which he put his hands on a female journalist’s knee.
Ms Leadsom is said to have accused Sir Michael of a string of inappropriate remarks when they were on the Treasury Select Committee together between 2010 and 2012.
As well as the “hands” comment to Ms Leadsom, he is accused of making comments of a sexual nature about other MPs on the committee and members of the public who attended hearings.
While the ex-Defence Secretary denied the claim that he made the comment to Ms Leadsom, The Sun reports he admitted making other comments during committee meetings that may have been inappropriate.
On Wednesday after admitting that his behaviour had “fallen below the high standards required” as a Defence Secretary, he announced his resignation.
A Downing Street spokesman would not get into a conversation over whether anything had been passed over from Ms Leadsom, but a source later denied she had asked the Prime Minister to consider sacking Sir Michael.
Ms Leadsom is herself leading the Government’s drive to push for new rules and systems of support for staff in Parliament who fall victim to sexual harassment.
Theresa May has faced a backlash after appointing former chief whip Gavin Williamson, who has never held ministerial office, to replace Sir Michael.
Tory former defence minister Anna Soubry said: “It does rather look like he picked himself a plum job.”
Ms May has called a meeting of all party leaders on Monday to agree a new system of dealing with abuse complaints in Parliament.
Meanwhile, the Prime Minister released a new code of conduct for all Conservative Party representatives, including a new complaints procedure with a hotline for reporting potential breaches.
For the first time, an investigation panel will include an independent member and a more detailed process, a letter to Commons Speaker John Bercow said.
Ms May called on other leaders to help her deliver a “serious, swift, cross-party response” to the problem, allowing complainants to take their concerns to a single body, regardless of the party of the alleged offender.
The letter rebuffed Mr Bercow’s suggestion that policing MPs’ behaviour should primarily be a responsibility for the political parties, pointing out that some MPs have no party affiliation – including the Speaker himself.
“It cannot be right, when dealing with serious issues relating to behaviour in Parliament, that vulnerable or concerned people are expected to navigate different grievance procedures according to political party,” Ms May said.
“Neither can it be right that such difficult issues themselves are dealt with on a party-political basis, or that no support should be provided for those with no political or party affiliation.”
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