But the former Labour deputy leader insisted that she recounted the joke in order to show that antisemitic humour was “no laughing matter”.
In a discussion about unacceptable subjects for comedy on BBC1’s This Week, Ms Harman said she had been branded “humourless” in the past for complaining about offensive jokes. And she went on to tell the joke as an example of the kind of material she objected to.
But her claim that presenter Andrew Neil would find the tasteless quip funny was rejected by the broadcaster, who turned his back on her and told her to “be quiet”.
Ms Harman said: “I’ve long been accused of being a humourless feminist and I’ll give you two examples that I protested about because they were offensive and hurtful.
“So, this was a Guy’s Hospital Rag magazine back in the day and people like Andrew say that these things are perfectly all right.” She then repeated one of the jokes, adding: “That’s not funny.”
Mr Neil responded: “We’ll stop with that one example and we won’t bother with the minute’s silence that you would dare to think what I would think about that, because you have no knowledge of that at all.”
As he turned to speak to another guest, the former Labour deputy leader attempted to interrupt in order to justify her decision to repeat the joke, only for Mr Neil to tell her: “Be quiet.”
The broadcaster later said of the incident on Twitter that he was “appalled and even a little bit upset by what she said”.
Mr Neil wrote: “What was wrong was 1) Even to tell that so called joke on live TV. 2) Claim I would like the joke. Appalling on both counts.”
The chief executive of the Jewish Leadership Council, Simon Johnson, demanded an apology from the Camberwell & Peckham MP for what he termed “a staggering error of judgment”.
“I cannot recall being so disappointed in a politician,” said Mr Johnson.
“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 judgment.”
In a tweet released following Mr Johnson’s call for an apology, Ms Harman said: “Anti-Semitic ‘jokes/banter’ perpetuate discrimination & hatred. No laughing matter.”
She added a link to an excerpt from her autobiography A Woman’s Work, in which she said that after complaining about the joke to Guy’s Hospital and referring the matter to the Director for Public Prosecutions, she was accused of “over-reacting and being humourless” by a newspaper.
Ms Harman’s words sparked condemnation from Twitter users, with some branding it “appalling”.