Jeremy Corbyn and Binyamin Netanyahu don’t have much in common, but both have something to gain from denouncing the other. For the Labour leader, a debate about the excesses of Netanyahu’s government since 2009 is safer ground than answering questions about his wreath-laying trip in Tunisia in 2014. On 13 August, Corbyn seemed to contradict an earlier line from the Labour press office about whether he knew that the architect of the massacre of 11 members of the 1972 Israeli Olympic team was being commemorated at the ceremony. Newspapers promptly ran his quote – “I was present at that wreath-laying, I don’t think I was actually involved in it” – next to a picture of him holding a wreath. Netanyahu’s tweeted criticism of his actions allowed Corbyn to move the discussion on to Israel’s killing of protesters in Gaza.

For Netanyahu, too, the row offers a respite from domestic woe. Israel’s new Nation-State law has been widely condemned for its disenfranchisement of the country’s non-Jewish citizens. It makes Hebrew the country’s official language, thereby downgrading Arabic, and states that Jews have a “unique” right to self-determination.

The law was hastily drafted to unify Netanyahu’s fractious coalition, and squaring up to Corbyn has a similar benefit. It allows the Israeli prime minister to dust off one of his most politically lucrative messages: European politicians do not have Israel’s best interests at heart and only his brand of militaristic belligerence can keep the small Middle Eastern state secure. The row over Labour’s tolerance of anti-Semitism as a whole is a more persuasive advert for Zionism than Israel’s present prime minister, however.

In the UK, the blunt truth is that accusations of anti-Semitism will move no votes outside the 300,000-strong Jewish community – just as few non-Muslims are exercised by Islamophobia within the Conservative Party. The polls have remained static throughout the latest row, as they have every time the topic has received widespread attention.

For Labour, the main damage is in the opportunity it has lost this summer. The party had prepared a recess campaign – “Build it in Britain” – covering nationalising the utilities and its plans to use Whitehall’s procurement powers to reshape the British economy. The leader’s office wanted to use these themes to peel off Leave voters disaffected by Theresa May’s Chequers proposals. That campaign is still going ahead – Corbyn returned from his summer holiday this week to attend a rally in Stoke – but it will receive limited attention.

Corbyn could, in theory, end the current row immediately by adopting the full International Holocaust Remembrance Alliance (IHRA) definition of anti-Semitism and repudiating many of his old alliances and positions. But there is as much chance of that as there is of him joining the Conservative Party. While he is perfectly capable of compromising on domestic issues – the rate of tax, maintaining some welfare cuts – foreign policy is another matter.

The arms trade is a case in point. On Heathrow expansion, Corbyn bowed to the interests of Unite and the GMB, which represent members in both the catering and aerospace industries, and offered a free vote on the third runway. However, Labour’s 2017 manifesto committed the party to an immediate and indefinite freeze on the sale of arms to Saudi Arabia and a cooler attitude towards the arms industry as a whole, despite the large number of Unite and GMB members it employs. This reflects Corbyn’s own long-standing position. As one of his longest-serving allies once reflected to me, “Jeremy would much rather be foreign secretary than prime minister.”

This realisation discomforts many at the top of the party, who fear that Corbyn’s foreign policy preoccupations could keep him out of Downing Street, never mind the Foreign Office. The party’s power brokers nominally share the Labour leader’s foreign policy objectives, but the industries and workers they represent come first. The trades unions Usdaw, Unison and the GMB are all affiliated to the Palestine Solidarity Campaign, but all have publicly called on Corbyn to abandon his opposition to the full IHRA definition of anti-Semitism, which Corbyn believes places excessive restrictions on criticisms of Israel.

At present, Labour’s big trades unions are bound to the party’s leader by two things: the first is his own popularity within the party, which remains undimmed. The second is that his domestic agenda is full of policy goodies for them. Hence the appeal in some circles for “Corbynism without Corbyn”: keeping his domestic agenda, but discarding his foreign policy baggage.

That hope will remain unfulfilled, however. Corbyn’s inner circle know that the voter coalitions he built to win the Labour leadership and fight the general election would not necessarily transfer smoothly to another member of the Labour left.

According to surveys of the party rank-and-file conducted by Corbyn’s internal opponents, there are more former Liberal Democrats among the activists who currently back him than there are supporters of the Greens, let alone the parties of the far left. Any attempt to hand over to a younger Corbynite could be interrupted by a less left-wing candidate on the fringes of the project, such as Angela Rayner, Emily Thornberry or Keir Starmer.

In a general election, meanwhile, any new Labour leader would need to be impeccably socially liberal (just look at what happened to Tim Farron) while also appealing to Labour Leave voters, an impressive feat that Corbyn has so far managed to pull off. And that is the real cause of anxiety on the Labour left as this long, hot summer ebbs away. They know that Corbyn is an asset – but they also know that he is a liability.