Speaker John Bercow has allowed time for a discussion in the Commons about his conduct following accusations of bullying.

Green Party co-leader Caroline Lucas has been granted an urgent question about the treatment of House of Commons staff.

Her intervention came as the Clerk of the House of Commons David Natzler promised to “revisit and renew” the grievance process and called for a “culture free of bullying and harassment” in Parliament.

It follows claims by BBC Two’s Newsnight about alleged bullying of women officials responsible for running the business of the House.

Ms Lucas is expected to ask Leader of the House Andrea Leadsom for an investigation and for the new independent complaints system announced last month to be extended.

Currently the complaints system only covers MPs’ staff and not those – like the clerks – who are directly employed by the House.

Ms Lucas said she was pleased her urgent question had been granted and asked MPs to focus on “those affected”.

The Brighton Pavilion MP said: “This is not about settling old political scores.”

She added: “People working in Parliament should be able to work without fear of intimidation or bullying – and today I’m calling for every member of staff to be given the best possible protection.

“It’s clear that all of those working in these buildings should be afforded equal protection – and I’m demanding that changes are made to urgently move all workers on to the new independent complaints and grievances procedure.

“It’s also crucial that historic complaints of bullying are heard under the new procedures too – and that decisions on sanctions are not in the hands of MPs.

“Parliament must be a safe workplace – where there is zero tolerance of bullying and harassment.

“I hope the changes are made swiftly to end this discrepancy in protections of staff, and to best protect them in the future.”

Meanwhile, the House of Commons’ senior official promised a review of the grievance process and apologised for the response to the latest allegations.

Mr Natzler said the Commons’ initial response “got it wrong in giving the impression that we were in denial” about the situation, adding “I wholeheartedly apologise for that”.

“There is no doubt in my mind that there are unresolved issues over bullying and harassment which need to be addressed,” he said.

He added that “we must look at our policies and see how we can improve them”, including a separate process for claims of sexual harassment.

“The only ultimately acceptable outcome will be a workplace culture free of bullying and harassment,” he said.

“I am conscious that revised procedures and processes are no substitute for cultural change.”

He acknowledged that “where things have gone wrong in the past they have not always been properly dealt with” but “they must, and will, be properly addressed in the future”.

Separately, critics of the Speaker are also considering whether to table a Commons early-day motion calling for an inquiry into the allegations.

Such a move would not normally result in a formal debate but could be a way to gauge support for any effort to oust the Speaker.

Tory Andrew Bridgen is understood to be in talks with Labour MPs about a possible cross-party motion.

The Newsnight report included a claim that Mr Bercow shouted at and undermined his former private secretary Kate Emms, eventually leading to her being signed off sick.

Mr Bercow has denied the allegations against him, as have the two other MPs named by the programme – Labour’s Paul Farrelly and Conservative Mark Pritchard.