Mrs May joked at the end of the pair's exchange today: "I've got some advice for the Right Honourable Gentleman - look behind you!
"They are not impressed and neither is the country!"
Mr Corbyn then shook his head and muttered "stupid woman" under his breath.
Watch it here:
About one hour after the incident, Corbyn returned to Commons. He denied being sexist and a misogynist.
John Bercow, the Commons speaker, made Commons statement about the “stupid woman” row.
He says he has watched the video. It is easy to see why people think Jeremy Corbyn said “stupid woman”. He says that is the view of “lipspeakers” he has consulted at short notice.
Bercow says Corbyn was sitting down at the time, and so he was not being recorded. He says no-one complained about the remarks at the time. He says no one can be 100% certain what was said, including lipreaders. But he would what is said by an MP at face value.
Bercow invites Corbyn to make a statement and share his point of view.
This is what Jeremy Corbyn said in response.
"During prime minister’s question time today, I referred to those who I believe were seeking to turn a debate about the national crisis facing our country into a pantomime as ‘stupid people’.
Mr Speaker I did not use the words ‘stupid woman’ about the prime minister or anyone else, and am completely opposed to the use of sexist or misogynist language in absolutely any form at all.
I’m happy to place that on the record at your request this afternoon".