Commons speaker John Bercow allegedly called a former clerk a “little girl” because he could not find an envelope.
In an article published in HuffPost UK, Ms Bradshaw said Whitehall was “haemorrhaging” talent and in “danger of being drowned by politics again”.
“This is not only bad for public service, but it turns the patriarchy into a self-fulfilling prophecy in one of the most high-profile organisations in the country,” she said in her contribution to the damning Cox report, which shed light on the environment in Westminster.
“The House of Commons Commission will have a large role in what happens next.”
Recalling one particular incident when the Mr Bercow was just a regular backbencher, she said he “screamed at me and called me a ‘little girl’ simply because he had been unable to find an envelope (which was exactly where I said it was, for the record)”.
Ms Bradshaw said she knew of dozens of former colleagues who had been bullied, assaulted and abused while working in parliament and called for change.
“The Cox Report should be a pivotal moment in parliament’s evolution into a modern workplace and those of us that contributed to the inquiry felt relieved and vindicated that we had finally been believed when we read the report and recommendations,” she wrote.
“But there is already talk that the report could get kicked into the long grass and the tribal warfare surrounding the speaker, and Brexit, have meant that this issue that has affected so many lives and careers is in danger of being drowned by politics again.”
A spokeswoman for Mr Bercow vehemently denied the allegations, saying he has “absolutely no recollection of this alleged incident – and it’s not, in his experience, the sort of statement he would make”.
Mr Bercow has been under pressure from Conservative MPs to step down after a probe by High Court judge Dame Laura Cox found a culture of “deference, subservience, acquiescence and silence” had been able to thrive.
She said radical changes were needed at a senior level, adding that it was “difficult to envisage” how the reforms could be delivered under the current senior Commons administration.
Signs reminding MPs not to “abuse” their power are being put up around the Houses of Parliament.
Mr Bercow had originally promised to quit amid the bullying row but as things escalated he reportedly told friends he would see out the Brexit process before quitting in June 2019.
Tory MP Anne Main said: “It’s the old adage that the fish rots from the head, and the leadership failings that have been highlighted in this report are extremely worrying.
“If this report has identified senior leadership failings … no one should be involved in this process who has been potentially linked to being part of the problem in this process.”
But shadow foreign secretary Emily Thornberry insisted it was “absolutely not the time to be changing speaker” and pointed to uncertainty over what would happen next with Brexit.
Additional reporting from PA
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