This week, Lord Levy warned that, unless the Labour leadership gives "a clear and unequivocal message" that antisemitism "in any form" would not be tolerated, he might have to leave the Labour Party.
You might have thought Labour leader Jeremy Corbyn would be shocked to hear this from a Jewish Labour peer. Instead he seemed angered by it.
"Lord Levy clearly hasn't been listening", he told Sky News. "I've absolutely condemned antisemitism; I've condemned Islamophobia, I've condemned any form of racism anywhere within our society".
This is a familiar refrain. Corbyn always condemns antisemitism as part of a package with Islamophobia and racism. He never speaks of antisemitism alone, as a specific problem needing its own response.
It suggests that he sees antisemitism as a product of the far-right bigotry that also generates hostility towards Muslims, migrants and other minorities in our multicultural society.
This is why, when Sky News asked him about antisemitism, he mentioned physical attacks on Muslim women in his constituency and talked about "the kind of decent inclusive society that we all want to live in". This misses the point. Nobody doubts that Corbyn wants to build an inclusive, diverse society. He is genuine in his hatred of far-right antisemitism and is rightly proud that his parents opposed Oswald Mosley at Cable Street.
Rather, the concern is whether British Jews can remain comfortable as members of Corbyn's Labour Party. At the 2009 meeting when Corbyn welcomed his "friends" from Hamas and Hizbollah, he also said "We are opposed to Zionism and what Israel is doing towards the Palestinian people... They can't live if you've got Zionism dominating it all."
The juxtaposition suggests that Corbyn would be more comfortable breaking bread with his "friends" from Hamas than with the "Zionists" of Labour Friends of Israel.
Corbyn has also argued that there is "a wider pattern of demonising those who dare to stand up and speak out against Zionism" - demonising them as antisemites, of course. Perhaps this explains his irritation in the interview at being asked about Lord Levy's comments.
The distinction between anti-Zionism and antisemitism is not so easy to maintain. The far-right antisemitism that Corbyn recognises and opposes is a fringe problem today compared to when his parents marched against it in the 1930s.
Instead, the antisemitism that concerns British Jews increasingly comes from other places. It comes from jihadists who want to kill Jews, and Islamists who think Mossad was behind 9/11. It comes from conspiracy theorists who believe Zionist money controls Washington DC and Trotskyists who see bourgeois Jews as a class enemy.
Some of these people inhabit the same left-wing, anti-war, pro-Palestinian spaces where Corbyn has spent a life-time.
While criticism of Israel is not antisemitic, here there is an antisemitic anti-Zionism that may have begun as a genuine desire to support the Palestinians but is now characterised by conspiracy theories and old antisemitic ways of thinking about Jews."
These ideas are now appearing in the Labour Party and it is Corbyn's responsibility to deal with them. Acknowledging that there are specific strains of left-wing and Islamist antisemitism, different from the more familiar far-right variety, would mean opening up his own political hinterland to an uncomfortable critique.
It is easier for Corbyn to repeat the mantra that he opposes antisemitism, Islamophobia and racism. As he told Sky News, he has said this seven times since becoming leader. He will probably say it again before too long, and all three are certainly worth opposing.
But until he acknowledges that this problem involves a different type of antisemitism, one that lurks much closer to home, it is unlikely that Lord Levy will get the kind of reassuring message that he wants.