In video footage taken at the end of the event at which Shami Chakrabarti’s report into Jew hate in the party was published, Mr Corbyn is shown chatting with Mr Wadsworth.
When Mr Wadsworth appears to be pushed as people leave the room, Mr Corbyn says: “Sorry about that.”
Mr Wadsworth replies: “I outed Smeeth, bloody talking to the Torygraph.” Mr Corbyn does not respond.
The Labour leader also appears to say: “I sent you a text.”
Mr Wadsworth later said he had no idea Ms Smeeth was Jewish.
It has also emerged that Emily Thornberry, Labour’s Shadow Foreign Secrerary, rang Mark Regev, Israel’s ambassador to Britain, to apologise for the confusion over Mr Corbyn’s comments regarding Islamic states.
Yiftah Curiel, the Israeli embassy press attaché, tweeted: “.@AmbMarkRegev welcomed @EmilyThornberry's unequivocal apology following @jeremycorbyn's unacceptable remarks.”
Journalists at the event believed they had heard Mr Corbyn say: "Our Jewish friends are no more responsible for the actions of Israel or the Netanyahu government than our Muslim friends are for the self-styled Islamic State".
Subsequently, it became clear that what Mr Corbyn had actually said was "Our Jewish friends are no more responsible for the actions of Israel or the Netanyahu government than our Muslim friends are for the self-styled Islamic states or organisations."
Seamus Milne, Mr Corbyn's director of communications, contacted the JC to explain that Mr Corbyn was in fact comparing Israel to "states like Iran, Pakistan, Hizbollah etc".
This article has been amended to update the headline
