Calling for urgent action, Sir Lindsay suggested staff should no longer be employed by the parliamentarians they work for to address a series of “serious allegations”.
He was considering moving to an outside body employing aides as Parliament’s reputation was feared to have hit a new low.
Writing in the Observer, Sir Lindsay said: “I believe it is time we reviewed our working practices, and particularly whether it is right that individual MPs are the employers of their staff. Should someone else – or an outside body – employ the staff, as long as the MP has the right to choose them?
“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.
“At the end of the day, I want to make sure that everyone feels they have support and somewhere to turn – and to make this house not only a safe and inclusive place to work, but a model for other legislatures.”
His bid for change was echoed by Andrea Leadsom, the former leader of the Commons, who in 2018 spearheaded the creation of the Independent Complaints and Grievance Scheme (ICGS), which looks into claims of bullying and sexual harassment.
She told The Sunday Times: “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 an end.
“It’s only when you see people getting done for being blind drunk and subject to the appropriate sanctions that people will start to think twice about their behaviour.”
Meanwhile, Tory party chairman Oliver Dowden reiterated a commitment from Boris Johnson to ensure half of Conservative candidates for the Commons are women.
In an interview with the Sunday Telegraph, Mr Dowden said the Tories need to ensure their candidate list “reflects the fact that half the population are women”.
Around a quarter of Conservative candidates at the 2019 election were women, but Labour managed to ensure women represented more than half of its candidates.
Earlier this week, Culture Secretary Nadine Dorries suggested ensuring “a majority of women” in Parliament could help tackle Westminster sleaze.
A series of damning developments has dogged the Commons in recent weeks.
Three Cabinet ministers are among 56 MPs reportedly facing allegations of sexual misconduct that have been referred to the Independent Complaints and Grievance Scheme.
Senior Labour MP Liam Byrne is set to be suspended from the Commons for two days for bullying a member of staff.
David Warburton had the Conservative whip withdrawn after allegations of sexual harassment and cocaine use emerged.
Former Tory Imran Ahmad Khan was resigning after being convicted of sexually assaulting a 15-year-old boy.