Last week, a new report found that 60% of the British public believe at least one conspiracy theory. The result of a six-year study spanning nine countries, the report showed conspiracy theory belief is higher among both Trump and Brexit supporters.

Entirely coincidentally (or was it? Who really knows… ) a small, cross-party Labour group including the Jewish Labour Movement, Socialists Against Antisemitism, Momentum, Open Labour and Labour First last week protested against a David Icke show in Watford, part of a tour. You might remember Icke as the footballer turned sports presenter turned believer-in-lizards – or rather, shape-shifting interdimensional reptilians known as “Illuminati”, who have taken human form and hijacked the world.

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I was unaware he was touring globally and packing 2,000-person capacity venues until this year when I saw the actor Marlon Solomon’s stand-up show on the subject of conspiracy theories and how they infiltrate the left. Like Solomon, the Community Security Trust (CST) – the charity set up to protect the Jewish community – has called out Icke’s constant referencing of “Rothschild Zionism”, with an article on their website last year describing him as “essentially a hate preacher with a 21st-century spin on a very old antisemitic conspiracy theory”. Icke has refuted such claims, insisting that he is not talking about Jewish people when he talks about Zionists.

Described as a professional conspiracy theorist, Icke’s work covers a range of subjects: pro-Brexit to pro-Assad, anti-Israeli to anti-vaccinations. It’s all packaged in a cosmic spiritual vibe of “infinite awareness”, which may explain why, according to some of those picketing Icke’s show last week, his audience includes a mix of neo-Nazis and New Age hippies – though it’s not clear what either cohort makes of his claims that the Queen is a lizard.

Unhelpful is the tendency to dismiss conspiracists as outlandish and laughable

Icke may, however, have achieved what others have failed to do: unite Labour’s often fractious intra-party groups over the common cause of tackling the conspiracists in its midst. While more common on the right of politics, the draw of conspiracy theories for the left lies in the frequent talk of establishment elites with undue global influence. You can see how this might overlap with the anti-capitalist ideas of the “We are the 99%” movement, though that doesn’t mean a critique of politics and capital is the same as a conspiracy theory. The Guardian reported as a “widespread conspiracy belief”, shared by 44% of people, one of the conspiracy survey’s polled statements: “Even though we live in what’s called a democracy, a few people will always run things in this country anyway.” However, even the survey’s authors question whether this is actually a conspiracy theory, rather than a reflection of a public sense of distrust and of not being heard.

Also unhelpful is the tendency to dismiss conspiracists as outlandish and laughable. We assume that conspiracy theories (which fuelled the most deadly antisemitism of the past century, culminating in the Holocaust) are no longer dangerous because they’ve been banished to the crank fringe and are just too daft. And yet here we are, with a malicious antisemitic theory around George Soros repeated by global politicians. And with a large chunk of the British population believing that there really is a Muslim plot to take over the UK, 31% of leave voters (and 6% of remain voters) believe the “great replacement” conspiracy theory of immigration as a plot to make Britain a Muslim majority country – a pet theory of the far right. As the CST’s Dave Rich, author of The Left’s Jewish Problem, points out, these might be crank theories but they aren’t fringe any more.

This much was evident in the response to Momentum, the grassroots group of Jeremy Corbyn supporters, taking part in the Icke picket and its accompanying video explainer – which provoked waves of anger and support for Icke on the group’s social media pages. This has also bled into Corbyn-supporting Facebook groups where Momentum has been denounced as, well, you can imagine: Zionist-funded pro-Israel stooges.

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Momentum had elsewhere been criticised for picking the low-hanging fruit of a lizard conspiracist, rather than taking on someone, say, closer to the Labour home. But this seems part of the strategy: using the Icke focus to enable a wider discussion of the use, amid the left, of classic antisemitic tropes involving, for example, the Rothchild family. It was perhaps also intended to flush out the conspiracists in their ranks – although the scale of the problem exposed has doubtless come as a surprise.

A small bright spot in all this is the sight of Momentum social media accounts now trolling the worst conspiracists with lizard emojis. Darker, but necessary, is the growing realisation that parts of the Corbyn-supporting social media apparatus are being used, by some, not just to support the Labour leader but, effectively, for antisemitism grooming.

• Rachel Shabi is a writer and broadcast news commentator