Mr Corbyn said that he would speak to the woman once he had finished.
The dark-haired woman was seemingly booed by the audience who had been chanting “Ooh Jeremy Corbyn” throughout the afternoon.
Jeremy Corbyn at the Durham miners gala
He told supporters his general election campaign was “not just the excitement of youth, not just the concerns of older people, it was a fundamental unease”.
He said: “Unease, that a society can go on in this direction with poverty and inequality alongside very rapidly rising huge individual wealth for a small number of people.
“I’ve got good news for the Tories: I know they’re living through a nightmare at the moment. I’m somebody, as you’re very well aware, that doesn’t get involved in personal abuse and would never exploit somebody else’s misfortune – so I want to help these Tories out of their nightmare.
“Feel free, at any time, to resign and we’ll have another general election.”