Speaker of the House Sir Lindsay Hoyle said “radical action” and a review of working practices was needed.

Meanwhile, former leader of the house Dame Andrea Leadsom backed setting up a human resources department.

The calls for reform come amid reports more than 50 MPs are facing allegations of sexual misconduct.

Multiple claims of bullying and sexual misconduct by MPs have emerged in recent weeks, culminating on Saturday in the resignation of MP Neil Parish – after he admitted to having twice watched pornography in Parliament.

Mr Parish told the BBC it had been a “moment of madness” and what he did “was absolutely totally wrong”.

His resignation will now trigger a by-election in his constituency of Tiverton and Honiton in Devon, which is a safe Conservative seat.

Among those calling for change is Ms Leadsom, the former leader of the Commons, who in 2018 spearheaded the creation of the Independent Complaints and Grievance Scheme which looks into claims of bullying and sexual harassment. Mr Parish’s case had also been referred to the ICGS.

Speaking to the Sunday Times, she said she believes the ICGS is still fit for purpose, but one key problem the scheme faces is it has not been able to employ a sufficient number of specialist investigators.

She said: “Things haven’t changed and that’s because there aren’t enough cases coming through and it’s taking too long for investigations to come to and end.

“It’s only when you see people being blind drunk and subject to the appropriate sanctions that people will start to think twice about their behaviour”.

She said Parliament should have a human resources department for staff.

Meanwhile, writing in the Observer, Sir Lindsay said he wanted to ensure Parliament was a “safe and inclusive” place to work and people felt supported and the serious allegations which have emerged must be addressed as a “matter of urgency”.

He also questioned whether MPs should be employers of their own staff and asked whether an outside body or other alternative could act as employer, as long as the MP was able to choose their staff.

This proposal for staff not to be employed by parliamentarians would mean new staff being “employed on standard terms and conditions”, he said.

Sir Lindsay wrote: “In my opinion, it is time to consider radical action, and review structures and processes that could make a difference.

“Some serious allegations have been made, and we must address them as a matter of urgency. It is imperative we do the right thing by staff and MPs as well.”

He added that work was under way to establish a “Speaker’s Conference” as soon as possible to consider these issues and suggested looking at practices in other parliaments around the world.

Meanwhile Oliver Dowden, the Conservative Party chairman, repeated a commitment from Boris Johnson to ensure half of Conservative candidates standing in the next election are women.

He told the Sunday Telegraph the Tories needed to ensure their candidate list “reflects the fact that half the population are women”. About a quarter of Conservative candidates at the 2019 election were women, while more than half of Labour candidates were women.

It has been a turbulent few weeks in Westminster, with three cabinet ministers reportedly among the 56 MPs facing allegations of sexual misconduct that have been referred to the ICGS.

As the beginning of April, Conservative MP David Warburton was suspended from the party pending an investigation into alleged sexual harassment.

A few weeks later it emerged Labour MP Liam Byrne is due to be suspended for two days from the Commons for bullying a former staff member.

And Tory MP Imran Ahmad Khan resigned from parliament after being convicted of sexually assaulting a 15-year-old boy.