The House of Commons could be brought into disrepute over the “disgraceful” way a damning report into bullying and harassment in Westminster is being taken forward, a former cabinet minister has said.

The Conservative MP Maria Miller, who chairs the women and equalities committee, called for “clarity” over when Speaker John Bercow would stand down, as she criticised the rate of change following Dame Laura Cox’s inquiry.

The inquiry recommended a shake-up of the senior leadership team, but Miller said the significant issues raised in the report appeared to be being “swept under the carpet”.

She said: “It’s absolutely disgraceful the way in which the Cox report is being taken forward, and that significant issues that she raised appear to be being swept under the carpet. I will continue to do everything that I can to make sure that there is an acknowledgement of the need to change the culture here.

“We cannot expect other organisations to be heeding or to take note and to act on campaigns like the #MeToo campaign if parliament is selective in the way that it chooses to implement the Cox report.

“At the moment it’s clear that a number of modernisation projects here have stalled and that is completely unacceptable and MPs will be taking the matter into their own hands.”

She said Cox was “absolutely clear” there would not be a change in the culture unless there was a change in senior management – including Bercow and the Commons Clerk.

“Sir David Natzler has announced that he will be leaving; we now need clarity as to when the Speaker will be leaving.

“It is difficult to explain to the businesses in this country that are being criticised for poor culture why parliament is not doing more on this, and it is also at risk of bringing the House of Commons into disrepute.”

Miller alluded to recent incidents in the Commons between Bercow and female Conservative MPs, including Nicky Morgan questioning his MP selection approach, and allegations that he called Andrea Leadsom a “stupid woman”.

She said many people in the Commons had been on the “receiving end of the Speaker’s displeasure”, and wondered whether he understood the “undermining” nature of some of his “outbursts”.

“The reason people will not speak out is fear of the Speaker: they are fearful of him and maybe they have just cause to be fearful of him,” Miller added. “He controls your ability to be able to contribute in the chamber, and secondly his outbursts can be very embarrassing and for some people even humiliating.”

She added: “Many female colleagues appear to have found themselves on the wrong side of the Speaker, which is curious.”

Some Labour MPs have spoken out in support of Bercow remaining as Speaker to see Brexit through the Commons, but Miller said that was “extraordinary” and “not justifiable”.

“There can never be any justifiable excuse for delaying change,” she said, “and certainly not in an organisation that should be leading the way.”

The Basingstoke MP, who quit the Commons reference group on representation and inclusion in October over Bercow’s chairmanship of the committee, said she hoped to “try and continue to press forward with the sort of improvements that seem to have stalled”.

She added that she wanted to “ensure that the new harassment and grievance processes are truly put in place and that outstanding issues that Laura Cox raised, particularly to do with historic allegations, are dealt with swiftly and not simply kicked into the long grass, which is what appears to be happening”.

A spokesman for the Speaker said: “The Speaker, alongside the entire House of Commons commission, has committed to swift and lasting change in response to Dame Laura Cox’s report and accepted its key recommendations. A number of changes have already been made in response to the report and the Speaker hopes and expects to see further such progress made in 2019.

“The Speaker was elected by the house in 2017 for the course of the parliament. In the event he has anything to say on his future plans, he will make an announcement to the house first.”