Thursday morning, embattled Labour Party leader Jeremy Corbyn gave a speech on anti-Semitism inside the UK Labour Party. Corbyn, currently fighting for his political life in the wake of accusations that he didn't work hard enough to stop Brexit, was announcing the conclusion of an investigation into recent accusations that the party's ranks had become full of anti-Semites.

The event was, not to put to fine a point on it, a mess. At one point, someone accused a Jewish MP of being part of a right-wing conspiracy. Corbyn himself made matters worse, by implicitly comparing Israel to ISIS in his speech.

"Our Jewish friends are no more responsible for the actions of Israel or the Netanyahu government than our Muslim friends are for those of various self-styled Islamic states or organizations," Corbyn said.

Yowch.

This has been a major problem for the Labour Party ever since late 2015, when left-wing firebrand Corbyn won the party's leadership election. In the past year, the party has had to deal with a handful of accusations of anti-Semitism within its ranks. These comments point to a broader problem with which the British left has been struggling: a perception that it is having trouble drawing the line between acceptable criticism of Israel and outright anti-Semitism.

So Thursday's debacle is part of a wider issue in British politics — and one that could not be reemerging at a worse time for Corbyn's political career.

When this controversy really took off: Naz Shah and Ken Livingstone

While the controversy surrounding the Labour Party and anti-Semitism has been around for a bit, it started getting a lot more attention in April 2016, because of some revelations about a Labour MP named Naseem "Naz" Shah.

In late April, Guido Fawkes, a UK website, published some pretty inflammatory screenshots from Shah's Facebook page. In 2014, before she was elected to Parliament, Shah shared an image that suggested that all Israelis should be "relocated" to the United States. "Problem solved," Shah wrote. It's not clear if this was meant literally, or as an over-the-top satire of the close US-Israel relationship. Either way, it's offensive.

Later that day, Guido Fawkes posted another screenshot in which Shah compares Israel to apartheid South Africa, the segregated American South, and Germany under Hitler.

The revelations kicked off a major dust-up. Leading UK politicians, including Prime Minister David Cameron, deemed her posts anti-Semitic, and called on Corbyn to suspend her from her position inside the Labour Party.

"Anti-Semitism is effectively racism and we should call it out and fight it whenever we see it," Cameron said, per the New York Times.

Right here, you see a major part of the controversy: defining when criticism of Israel becomes anti-Semitism. Read very narrowly, Shah's comments aren't talking about Jews outside Israel. But the issue here isn't that Shah is condemning UK Jews in Hitler-like terms, but rather that her attacks on Israel have been so vitriolic as to veer into what many see as anti-Semitic territory.

Initially, it looked like Shah might survive: She apologized promptly, and Corbyn refused to suspend her. But shortly thereafter, Corbyn reversed himself, suspending Shah.

Yet the saga wasn't over. Enter Ken Livingstone — the former London mayor known as "Red Ken" for his hard-line left-wing politics ("red" referring to the traditional Communist use of the color).

Two days after the Shah controversy began, Livingstone went on the BBC to talk about her suspension. His comments were ostensibly aimed at defending her, but merely ended up getting him into more trouble. He said that Shah's comments weren't anti-Semitic because "a real anti-Semite doesn’t just hate the Jews in Israel." He also said something curious about Hitler:

When Hitler won his election in 1932 his policy then was that Jews should be moved to Israel. He was supporting Zionism before he went mad and ended up killing six million Jews.

This reads like a somewhat strange defense of anti-Zionism: If Hitler was a Zionist, then anti-Zionism must not be the same as anti-Semitism. This is absurdly inaccurate — Hitler was never a Zionist — and also offensively links a movement supported by Jews with the most famous anti-Semite of all time. Alternatively, it could be read as simple Hitler apologia, which is how Labour MP John Mann saw it. He angrily confronted Livingstone, condemning him as a "Nazi apologist." Here's video:

.@JohnMannMP, chair of UK parliament's anti-Semitism group, confronts his own party official over his anti-Semitism: pic.twitter.com/rZ4LRQkF6Z — Yair Rosenberg (@Yair_Rosenberg) April 28, 2016

Corbyn promptly suspended Livingstone from the Labour Party. But by then, the idea that Labour had become a hotbed of anti-Semitism had become a major theme in the British press.

The bigger context: Labour's new leader has had to deal with a number of controversies surrounding Jews and Israel

The Shah-Livingstone saga would have been a big controversy under any circumstances. But this is a particularly massive deal because accusations of anti-Semitism have dogged the Labour Party ever since Jeremy Corbyn took control of it last year. The issue is not that Corbyn is personally anti-Semitic (he isn't), but rather whether he's insufficiently sensitive to a problem of anti-Semitism within his party's ranks.

Corbyn won the Labour equivalent of a primary last September, in an absolute stunner. He was an obscure left-wing backbencher going up against some of the Labour leadership's leading lights; when the race began, oddsmakers gave him a 100 to one shot at victory.

Corbyn's victory shocked the UK political class; he was far to the left of any leader of Labour since the 1980s, proposing to nationalize several major parts of the British economy. But his comments on Israel also raised eyebrows. Most notoriously, Corbyn once referred to members of Hamas and Hezbollah — both US-designated anti-Israel terrorist groups — as "friends," and invited Hamas representatives to speak in Parliament. Here are the comments, from a 2009 speech he gave as a patron of the Palestine Solidarity Campaign:

It will be my pleasure and honor to host an event in Parliament where our friends from Hezbollah will be speaking. I’ve also invited our friends from Hamas to come and speak as well. … So far as I’m concerned, that is absolutely the right function of using Parliamentary facilities.

Corbyn has tried to play down the "friends" comments, arguing that he was just saying all parties to a conflict should be involved in peace negotiations. But the comments were nonetheless controversial, especially since reporters unearthed that Corbyn had donated money to an organization run by a Holocaust denier (Corbyn claimed ignorance of his views) and had praised a preacher who claimed that Jews had foreknowledge of 9/11.

All of this led British Jews to be somewhat skeptical of the new Labour leader. A poll around the time of his election found that 67 percent of British Jews were "concerned" about him taking control of the Labour party.

Since then, a handful of anti-Semitism scandals in the Labour party have gotten a lot of attention. They include a Labour city council member being suspended for tweeting that "Adolf Hitler = greatest man in history," and the chairman of Oxford University's Labour club resigning because of a "poisonous" attitude toward Jews among its members.

This has led to some UK commentators and politicians arguing that Labour under Corbyn has developed an anti-Semitism problem.

"Jeremy Corbyn [is] a man who has shared a platform with a Holocaust-denier and who has set the tone of inaction against anti-Semitic outrages in his own party," Robert Shrimsley, managing editor of the Financial Times (who is himself a left-wing British Jew), writes.

"The more anti-Semitic Corbyn’s Labour is revealed to be, the more Jewish I feel," Eleanor Margolis writes in the center-left New Statesman.

After Shah and Livingstone, Corbyn admitted that there were a "very small number of cases" of anti-Semitism, but they had all been dealt with. Yet that wasn't exactly satisfying for Corbyn's critics.

The even bigger context: a controversy surrounding the left, Israel, and anti-Semitism

But this issue goes even deeper than Jeremy Corbyn. British Jews and others sensitive to anti-Semitism see these handful of anti-Semitic incidents as a possible trend: an indication that the British left has a real anti-Semitism problem. The reaction would probably be less pronounced if it had been only one incident instead of several, or if it had happened under another Labour leader without Corbyn's history. But the two have combined to bring fears of anti-Semitism to the fore.

More and more Brits — and not just conservatives — are arguing that Labour and the left more generally have an anti-Semitism problem. "Anti-Semitism never seems to go away. People have obviously chosen to associate with the Labour party in the growth of membership [under Corbyn]; some of those people have attitudes that are very outdated, that are prejudiced," Labour MP John Mann, who was shown on video confronting Livingstone, said in March.

Lord Michael Levy, a Labour member of the House of Lords (the upper house of Britain's Parliament), said in a BBC appearance that the party had a "serious problem" with anti-Semitism, adding that it seemed "more prominent" in Labour than in its rival Conservative party.

The crux of the case against Labour centers on the British left's attitudes toward Israel. Shrimsley puts it clearly in his piece on Corbyn:

There is no reason to believe Corbyn is an anti-Semite. But in his deep and legitimate support for the Palestinian cause, he has failed, in his alliances and actions, to draw a line over what is and is not acceptable. And this has been seen by others as a green light to bring their hatred out into the open. Holocaust denial, racist stereotyping, the casual usage of Nazi terminology, talk of Zionist conspiracies and the deployment of the word "Zionist" as a euphemism for Jew are now common among his supporters.

Labour's membership is relatively critical of Israel — polling data shows that Labour voters are more likely to sympathize with the Palestinians than Israel, while the reverse is true among Conservatives. That is, of course, a legitimate position, and the overwhelming majority of Labour criticism of Israel is not anti-Semitic. Nor, again, is there any reason to believe that Corbyn himself is an anti-Semite.

The problem, Corbyn's critics allege, is that his leadership has been insufficiently concerned with anti-Zionism merging with anti-Semitism — which is why his comments on Thursday that compare Israel with ISIS were such a huge error.

Members of the extreme left, empowered by Corbyn, have been invoking anti-Semitic stereotypes in their criticism of Israel or comparing Israel to Hitler. This language, the critics allege, is becoming more common. Anti-Zionism is being used as a vehicle for mainstreaming anti-Semitism.

"What of those who attack not Jews, but only Zionists? Defined narrowly, that can of course be legitimate," Jonathan Freedland writes in the Guardian.

"But Zionism, as commonly used in angry left rhetoric, is rarely that historically precise. It has blended with another meaning, used as a codeword that bridges from Israel to the wider Jewish world, hinting at the age-old, antisemitic notion of a shadowy, global power, operating behind the scenes."

Are these charges true? That's a very hard question to resolve. You could argue, as Corbyn and his supporters do, that these are just a handful of examples, that anti-Semitism existed before Corbyn and is no more endemic on the left than it is anywhere else.

"Given that an estimated seven-to-ten percent of the UK population doesn’t like Jews, the wonder would be if Labour, which with a total membership of some 400,000 is Britain’s largest political party, did not harbour a small number of anti-Semites within its ranks," Jamie Stern-Weiner argues in OpenDemocracy.

But then again, it's an awful lot of examples in a short period of time.

Regardless, one thing is clear: A significant number of prominent Britons see anti-Semitism as a growing problem on the UK left. That's not something Corbyn can just dismiss. It's a perception he's going to have to work to dispel.

But it's not clear he has the time. Just earlier this week, Corbyn lost a no-confidence vote among Labour MPs by a whopping 172-40, owing largely to the fact that refused to campaign hard against Brexit. The vote doesn't topple him, but it does suggest he doesn't have very much political support in his party. It'll be even tougher for Corbyn to weather the Brexit storm if he also has to deal with a resurgence in the anti-Semitism controversy at the same time.