Mr Green was accused of using the site in 2015 when his work email address appeared among the details of members that were leaked after a major hack.

He vehemently denied the claims at the time, saying: ‘It’s nothing to do with me. I have never registered for an account with Ashley Madison.’

Asked about Mr Green appearing on the list, a spokesman for the Prime Minister said: “I haven’t seen any allegations in relation to the First Secretary of State and I’m not going to comment on speculation in any way.”

The Cabinet office declined to comment on the allegation.

Mr Green is a  supporter of the Prime Minister and one of the few Remainer voices still in the cabinet. The claims could weaken Mrs May’s already precarious position.

The accusation is one of a slew of allegations of sexual misconduct from MPs that have emerged in the last few days, including a claim that international trade minister Mark Garnier asked his Commons secretary to buy sex toys and called her “sugar tits”.

Defence Secretary Michael Fallon was also forced to apologise for putting his hand on a female journalist’s knee.

The incident involved Julia Hartley-Brewer, who said she does not regard it as “anything other but mildly amusing”.

A spokesman for Sir Michael said: “He had apologised when the incident happened 15 years ago and both Julia and he now considered the matter closed.”

The revelations caoe as Parliamentary authorities draw up plans to allow victims of sexual harassment to report incidents “without fear”, with abuse allegations continuing to dominate Westminster.

Commons Speaker John Bercow met with senior parliamentary figures on the House of Commons Commission to plot a way forward as fresh claims of sexually intimidating behaviour emerged.

A spokesman for Commons Speaker John Bercow, who chaired the Commission meeting, said: “The Commission discussed the recent allegations relating to the harassment of staff, following today’s exchanges in the House of Commons.

“It recognised that the current processes for dealing with this required review and a more thorough understanding of how they are put into practice by political parties.

“The Commission therefore committed to urgent work, in concert with the key stakeholders, to identify a way forward which would command general confidence and enable people to speak up without fear or favour.”