Parliament must act to stop the “seemingly endless” allegations of sexual misconduct by MPs as political parties cannot be trusted to make it a safe place to work, two leading unions have warned.

As No 10 admitted Boris Johnson had known about allegations against Chris Pincher before making him deputy chief whip, the FDA and Prospect said politicians were time and again failing to “deal properly with sexual misconduct by one of their own”.

The unions, representing more than 1,000 parliamentary workers, wrote jointly to Lindsay Hoyle, the Speaker, urging parliament to take action after the scandal over Pincher, who resigned last week after reports that he drunkenly groped two men in a London private members’ club.

Johnson is under continuing pressure over the Pincher affair, after his spokesperson admitted on Monday that he was aware of general speculation before promoting the MP to deputy chief whip in charge of welfare of colleagues in February.

Despite last week saying the prime minister was not aware of “specific” allegations, No 10 conceded that Johnson had known of concerns about Pincher that were “either resolved or did not proceed to a formal complaint”.

But on Monday night the BBC reported that Pincher was investigated for inappropriate behaviour with the complaint upheld when he was at the Foreign Office as a minister in 2019-20, and that the prime minister was made aware of that incident.

Asked by the Guardian last Friday about whether there were misconduct allegations against Pincher when he was at the Foreign Office, a government spokesperson did not deny this, saying: “There are robust procedures in place for any members of staff to raise allegations of misconduct. It is longstanding policy not to comment on any matters involving individual cases.”

Pincher has denied other allegations that have emerged since the Carlton Club claims. It follows five previous sexual misconduct scandals involving Tory MPs this parliament, leading to pressure on Johnson to clean up his party’s culture.

These include Neil Parish, who watched pornography in the Commons; Imran Ahmad Khan, convicted of sexual assault against a child; and David Warburton, who is under investigation by parliament’s watchdog over three allegations of sexual misconduct towards women, which he denies.

An unnamed Tory MP was also last month arrested on suspicion of rape and other sexual offences, while Tory MP Rob Roberts had the whip suspended after an independent investigation found that he sexually harassed a junior member of staff.

Former Conservative whips have told the Guardian they were aware as far back as 2017 that Pincher on occasion drank too much and that he had been warned against getting himself in trouble. He quit the whips’ office in November 2017 after a claim by former rower Alex Story that he made unwanted sexual passes – and was later cleared by an internal party investigation.

Sky News also reported that Carrie Johnson, the prime minister’s wife, had questioned Pincher’s suitability to be a whip in 2017 when director of communications at the Conservative party. Her spokesperson was approached for comment.

In light of the Pincher scandal and the arrest of a Tory MP, who has not had the whip suspended, the FDA and Prospect asked Hoyle to act by looking at reform of parliament’s approach to sexual misconduct in his forthcoming Speaker’s conference – a forum for reviewing how the Commons works. They highlighted comments by Labour MP Luke Pollard that parliament is “not a safe place to work” and the “seemingly endless list of allegations of sexual misconduct by MPs”.

“Political parties of all stripes have proved time and time again that they cannot be trusted to deal properly with sexual misconduct by one of their own,” wrote Dave Penman, general secretary of the FDA, and Mike Clancy, general secretary of Prospect.

“If the parties will not act, then parliament must, by taking a zero-tolerance approach to sexual misconduct by MPs and by taking seriously its responsibility to provide a safe workplace for those working there.”

They said parliament has had its reputation “significantly damaged as a result of numerous well-publicised incidents of alleged sexual misconduct and misogyny perpetrated by politicians against parliamentary employees, constituents and others, including fellow MPs”, which has been worsened by the revelations in relation to Pincher.

They said it was hugely significant that parliament had shown a “lack of engagement” over these scandals, asking: “Does parliament, as an employer and public institution, have a view on the current crisis of misconduct and sexual misbehaviour? Does parliament have concerns that the potential risks to those who work and visit the estate are not being dealt with appropriately by political parties and the government? Does parliament believe that it has the powers it needs to address breaches of ethics and standards by MPs when the parties will not?”

They argued that the remit of the Speaker’s conference, agreed by the Commons last week, should be broad enough to address whether existing governance within parliament remained fit for purpose, and look in particular at the inability of parliament to exclude from the estate MPs under investigation for sexual misconduct.

They also called for training on bullying and sexual misconduct to be made mandatory for all MPs. The conference, made up of a committee of MPs, is currently planned only to deal with the employment arrangements of MPs’ staff, reviewing current working practices and conditions.

After the #MeToo scandal in Westminster, which brought down several cabinet ministers, parliament brought in an independent complaints and grievance scheme allowing victims to bring sexual harassment and bullying complaints to an independent investigator. However, political parties have since then used the independent complaints and grievances scheme (ICGS) as an excuse not to conduct their own investigations, and Jess Phillips, the shadow Home Office minister, has warned there is too much burden on victims to bring formal complaints. The scheme also only covers those who work in parliament and not alleged victims from outside Westminster, although visitors to the parliamentary estate or events relating parliamentary work are covered.

A House of Commons spokesperson said: “Sexual harassment has no place in the Commons. We take the safety of our staff seriously, and parliament’s behaviour code makes clear the standards of behaviour expected of everyone in parliament – whether staff, members of the House of Lords, MPs or visitors. There is zero tolerance for abuse or harassment.

“The behaviour code is supported by the independent complaints and grievances scheme, which provides for the investigation of complaints of bullying, harassment or sexual misconduct.”