Theresa May has written to John Bercow, the Commons Speaker, calling for the establishment of a new grievance procedure to deal with complaints of misconduct in Westminster.

The unprecedented step comes as high-profile politicians were accused of misconduct in reports on Sunday amid an increasing number of allegations of sexual harassment in the Palace of Westminster in the wake of the Harvey Weinstein abuse scandal.

In the letter – addressed to Mr Bercow and the leaders of all the major political parties – the Prime Minister said “it is important that those who work in the House of Commons are treated properly and fairly – as would be expected in any modern workplace”.

Ms May said that current procedures provided by the Independent Parliamentary Standards Authority do not “have the required teeth” as contractually an MP does not have to follow them.

“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 added.

The letter sent to Mr Bercow on Sunday continues: “The Conservative Party is determined to protect those staff who work for MPs but in order to do so effectively I believe that we must establish a House-wide mediation service complemented by a contractually binding grievance procedure available for all MPs irrespective of their party banner.

“It is vital that the staff and the public have confidence in Parliament and resolving this employment irregularity on a cross-party basis can play an important role in this.”

It comes after several reports of misconduct by politicians from all parties and the admission from Mark Garnier, a minister in the Department for International Trade, that he asked his secretary to purchase vibrators for him from a sex shop in Soho.

Mr Garnier, who is now subject to an investigation into whether he broke ministerial code, was also accused of referring to his former secretary as “sugar tits”. The MP for Wyre Forest said he was “not going to be dishonest” after Caroline Edmondson told The Mail on Sunday that Mr Garnier gave her money and waited outside the sex shop while she went into to buy two vibrators.

Ms Edmondson added that Mr Garnier had told her that one of the sex toys was for his wife while the other was for a female assistant in his West Midlands constituency.

“I’m not going to deny it, because I’m not going to be dishonest,” Mr Garnier said. “I’m going to have to take it on the chin.”

But the father-of-three denied the 2010 incident constituted sexual harassment and said the sex toys were bought after a Christmas lunch and the “vibrator shop was high jinks”. He said his “sugar tits” comment was part of “an amusing conversation” about TV show Gavin & Stacey.

In a separate report the newspaper also said former cabinet minister Stephen Crabb had admitted sending “explicit” messages to a 19-year-old woman he interviewed for a job in 2013, when he was Welsh minister.

The married MP, who resigned last year as Work and Pensions Secretary following reports of a similar incident, was quoted by the paper as saying he had been “foolish” but that there had been no sexual contact. “We exchanged messages which talked about sex but none of it was meant seriously,” he was quoted as saying.

“We met for coffee a few times and had a glass of wine once at the Commons, but nothing more. I accept any kind of sexual chatter like this is totally wrong and I am sorry for my actions.”

It is believed the Weinstein abuse scandal in Hollywood – involving more than 50 accusations of either sexual assault or harassment – has encouraged women in a number of professions to come forward and report information about sexual harassment and misconduct.

The Labour leader Jeremy Corbyn said last week that after the revelations about the Holywood producer, the issue of sexual harassment and abuse “is rightly being discussed much more openly”.

He added: “Sexual harassment is not of course confined to Hollywood. Misogyny and sexism are widespread problems across society. It exists and thrives in the corridors of power, including in Westminster.

“At this time, many women have felt more able to come forward and speak about abuse they have experienced.