The Commons speaker, John Bercow, should consider stepping back from the role while allegations that he bullied a female former staff member are investigated, senior MPs said last night.

Claims that the Buckinghamshire MP, who has been speaker since 2009, shouted at and undermined his former private secretary Kate Emms, eventually leading to her being signed off sick, were aired last week in a BBC Newsnight investigation. Tory Mark Pritchard and Labour’s Paul Farrelly were also accused of bullying. All three MPs deny the allegations.

Jess Phillips, who chairs the women’s parliamentary Labour party, and Caroline Lucas, co-leader of the Green party, said that at a time when parliament was desperate to improve its image and procedures, following the sexual harassment scandal there, the best way forward might be for Bercow to withdraw from some of his duties until the claims had been thoroughly looked into.

Phillips insisted Bercow had done much to help modernise the Commons and improve conditions for women in parliament, saying he had been “very good for women”. But “these accusations do not tally at all with my experience of John. In my dealings with him he has done a lot. He understands the issues. He has been really at the forefront of modernisation of the Commons.”

But, she added: “Having said that, clearly there has to be some kind of independent investigation. And it may be that he should consider stepping back until that has taken place.”

Facebook Twitter Pinterest Jess Phillips, the chair of the women’s parliamentary Labour party, has advised Bercow to withdraw from duties. Photograph: Fabio de Paolo/The Guardian

The latest controversy to hit Bercow will reach the Commons on Mondaywhen Lucas will seek to table an “urgent question” calling for an investigation and for the independent complaints procedure that was announced last month by Andrea Leadsom, the leader of the Commons, to be extended. At present it only covers MPs’ staff but she will call for it to cover others employed in parliament.

Lucas’s call places Bercow in a difficult position as it is normally the speaker who makes the decision whether permission to ask such questions is granted, after consultation and advice from Commons clerks.

Lucas said: “I think at the very least he should withdraw from that decision and that the three deputy speakers might judge on that.” There might also be a case for stepping back temporarily if an investigation is carried out.”

While many Conservatives dislike Bercow and want to find a way to oust him because they object to his manner and think he is biased towards Labour, others fear the constitutional damage that will result if successive speakers are removed.

Senior Labour MP Angela Eagle said that while she had been no fan of Michael Martin, Bercow’s predecessor who was forced to resign in 2009 over his handling of the expenses scandal, she had not been in favour of his removal in what was effectively a coup. Neither would she approve if there was a politically driven campaign to get rid of Bercow.

A senior Tory party MP said that if a vote of confidence in Bercow were held, the “vast majority” of Conservatives would vote for him to go.

“That would require Labour MPs and particularly women Labour MPs to demand one,” the senior Tory said. “Then if that happened I think he would be gone because there is not much love for him on our side of the House, to say the least.”