Mr Corbyn insisted that he had muttered “stupid people” during the final prime minister’s questions of the year in the House of the Commons.
The incident provided a further example of how Mr Corbyn has had a difficult 2018. Exactly one year ago he predicted that he would probably be prime minister within 12 months, but he has so far failed to force a general election despite Mrs May’s acute problems over Brexit, or to pull ahead in opinion polls.
One shadow cabinet minister said: “I don’t think we would win a general election at the moment.”
Since January Mr Corbyn’s net favourability ranking has fallen from minus 12 to minus 35, according to YouGov, the polling company.
“Not much has changed over the past year, but Jeremy Corbyn’s ratings are the exception. They have gone steadily down,” said Anthony Wells, research director at YouGov.
Mr Corbyn’s supporters argue his fortunes will rise again in an election campaign, and the Conservative party’s deep divisions over Brexit could yet propel Labour to power within months.
But while the political action is in parliament, Mr Corbyn has struggled to add to Mrs May’s troubles.
“A different Labour leader could have made things much, much more difficult,” said Keith Simpson, a backbench Conservative MP. “One colleague was saying that he remembered [then Labour leader] John Smith savaging [then prime minister] John Major in the 1992 parliament. Corbyn’s not very good.”
A case in point was Mr Corbyn’s hesitation over calling a vote of no confidence this week. He eventually did table a motion, but only in Mrs May as prime minister, not in the government as a whole. This meant the government could stop the motion from even being debated by MPs.
Mr Corbyn’s spokesman declined to comment.
The Labour leader’s popularity has long rested on his high-spending economic policies, as well as his avuncular image.
But the latter was badly damaged over the summer by months of allegations that he was slow to tackle anti-Semitism within the Labour party.
Using the term “stupid woman” would also dent Mr Corbyn’s image, and Tory MPs have demanded he apologise.
But Commons speaker John Bercow concluded on Wednesday there was no need for the Labour leader to apologise, saying that even professionals could not be “100 per cent certain” of Mr Corbyn’s words.
The Labour leader was defended by a Scottish National party MP, Joanna Cherry, who said he was victim of a “kangaroo court” and Tory “hypocrisy”.
But parliament is particularly sensitive to sexist and abusive language following months of revelations about bullying of parliamentary staff by MPs.
Mr Bercow’s stance infuriated Conservative MPs, many of whom believe he is biased in favour of Labour. “If it were one of my male colleagues on this side of the House who had used that expression . . . you, sir, would take action immediately,” Anna Soubry, a backbench Tory MP, told the speaker.
Andrea Leadsom, leader of the Commons, said Mr Bercow had recently called her a “stupid woman” and not apologised. Mr Bercow insisted he had dealt with that matter.
Mr Corbyn would not be the first MP to have called another a “stupid woman”. In July chancellor Philip Hammond, one of the cabinet’s leading Europhiles, used the term to describe Andrea Jenkyns, a Eurosceptic Tory MP. In 2013 the then foreign secretary William Hague applied it to Labour MP Cathy Jamieson.
The furore over Mr Corbyn’s alleged remarks overshadowed his attempts to criticise Mrs May’s decision to “recklessly” waste billions of pounds on preparing for a no-deal Brexit.
Mr Corbyn, a longstanding Eurosceptic whose Brexit policy has often seemed deliberately ambiguous to maintain Labour’s electoral coalition of Leavers and Remainers, has promised to negotiate a different withdrawal agreement quickly if he becomes prime minister.
But many of his own MPs are unconvinced and believe he will need to change stance, possibly to back the case for a second Brexit referendum, after MPs vote on Mrs May’s deal with the EU in January.
Additional reporting by Laura Hughes and Jim Pickard
Get alerts on House of Commons UK when a new story is published