When Ms Harman tried to explain why she had told the joke – which referred to Jews being gassed to death during the Shoah – Mr Neil told her: “Be quiet.”
Her remarks sparked an immediate furious response from viewers on social media.
On Friday morning, Simon Johnson, chief executive of the Jewish Leadership Council, said: “I cannot recall being so disappointed in a politician.
“Harriet Harman must surely know better than to repeat a vile Holocaust joke, irrespective of the point she was trying to make.
“She must apologise and do so quickly. It is a staggering error of judgement”.
Ms Harman has served as MP since 1982, in roles including temporary leader of the opposition, deputy leader of the Labour Party, and in government as Minister for Women and Equalities.
