The video was taken from the Palestinian Return Centre and published by the MailOnline.
Corbyn's also faced criticism from a number of Labour MPs but a spokesman said he was quoted out of context and is 'totally opposed to all forms of antisemitism and is determined to drive it out from society'.
The Council of Christians and Jews said comments like this were working against the works it was doing.
In a statement, it said: "CCJ deeply regrets the comment made in 2013 by Jeremy Corbyn that British Zionists have - no sense of English irony - despite having 'lived in Britain all of their lives'. This kind of old antisemitic trope that Jewish people hoped they would never hear again, seeks to imply that Jewish people in Britain are somehow outsiders who don't really belong. Unfortunate remarks of this kind can only make Jewish people feel very unwelcome in their home.
"CCJ has worked to strengthen bridges between Christians and Jews for over 75 years through mutual respect and understanding. In particular as Christians and Jews together, CCJ seeks to educate against and combat antisemitism in all its forms. Community relations are deeply undermined when leading public figures make remarks of this nature."
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