Conservative MPs claim he made the remark about the Commons Leader Andrea Leadsom – and used foul language – after launching a tirade against the government.
Mr Bercow is said to have made the remarks – which he has not denied – after Prime Minister’s Questions as Transport Secretary Chris Grayling was about to make a statement on railways.
Labour’s chief whip Nick Brown rose to complain that the opposition had been denied a copy of the statement and that it was being made to cut into time allocated for an oppposition debate.
The speaker then responded with an angry rant against the government, much of it directed at Ms Leadsom, and MPs claim his insult was then delivered under his breath.
One unnamed MP who claims to have heard Mr Bercow’s aside told The Daily Telegraph: “He said ‘stupid woman’ and went on to say either ‘f****** useless or f****** outrageous.
“But I’m clear that the words ‘stupid woman’ were said, and I am clear that the word ‘useless’ was said. I thought what I was witnessing was entirely outrageous.”
Responding to the latest accusation, a spokesperson for the speaker made no attempt to deny that he used the words attributed to him or that the target was Ms Leadsom.
“Wednesday was an unusual and controversial day in how business was handled in the House by the government and some strong and differing views were expressed on all sides on the subject,” the spokesperson said.
“The speaker treats his colleagues with respect and strives at every turn to facilitate the House of Commons.”
A Commons source told the Sun: “Mrs Leadsom did not hear the remark herself but was left stunned when told about it by outraged colleagues.
“But she is very keen to rise above it and not let it distract from other very serious and worrying claims about bullying made in parliament.”
The accusation comes less than two months after Mr Bercow branded Boris Johnson “sexist” for calling Labour’s Emily Thornberry “Lady Nugee”, her married name.
It also comes as the speaker battles to keep his job amid calls to quit over allegations that he bullied and abused two former members of his Commons staff.
In his attack on the government over Mr Grayling’s statement, Mr Bercow said the Transport Secretary had “beetled up to the Chair” and said his announcement was commercially sensitive.
But he said it was “highly undersirable” for there to be statements on substantial matters on days for opposition debates.
On this occasion, Labour had tabled two motions, on Grenfell and Brexit.
And then, turning to face the Leader of the Commons, he said: “One looks to people traditionally with responsibility for safeguarding the rights of the House, of whom the Chair is one but not the only one, to take these matters very seriously.”
He said it was an “undesirable state of affairs” and if it were to happen again MPs and other interested parties would view it as “an abuse”.
He added, in a clear reference to Ms Leadsom: “I hope that message is heard loudly and clearly on the government front bench, at the highest level, by the people by whom it needs to be heard.”
And appearing to threaten the government, Mr Bercow said: “If I have to make this point again on future occasions and to use the powers of the Chair to facilitate the rights of this House in other ways, no matter what flak emanates from the executive, I will do so in the future, as I have always done over the past nine years, and no one and nothing will stop me doing my duty by the House of Commons.”
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The incident happened just hours before a committee of senior MPs blocked an inquiry into allegations Mr Bercow bullied two former private secretaries, Angus Sinclair and Kate Emms.
The Commons Committee on Standards voted three-two against allowing parliament’s commissioner for standards to investigate the allegations, which Mr Bercow has denied.