A pro-Israeli British charity leading a fierce campaign against the Labour leader Jeremy Corbyn over anti-Semitism is being investigated by the Charity Commission and police over suspicion of engaging in party-political activity.

The Campaign Against Anti-Semitism (CAA) – which was formed during “Operation Protective Edge” in the summer of 2014 when over 2,000 Palestinians, including 551 children were murdered by Israeli missile attacks and shelling of civilian areas – has been accused of inciting death threats against Corbyn through its campaign, including a petition in which the pro-Israeli organisation called for the Labour leader to be removed from his position.

Some of the comments on the petition posted by people who signed it label Corbyn “a piece of terrorist loving anti-Semite scum” and “a dirty Nazi … persecuting the Jews who are peaceful people unlike the immigrants he wants to flood the country with.”

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Another person posted: “Let’s get this bastard” while another accused the Labour leader of “hating white people.”

The Metropolitan Police is reported to have confirmed that it is investigating the CAA and the petition under the Malicious Communications Act after receiving a number of complaints. A Met spokesperson is reported to have said that no arrests have been made and that the investigation is ongoing.

The CAA is described by its critics as a “McCarthyite propaganda organisation whose aim is to smear and libel opponents of Israel’s apartheid regime”. In a petition calling for the CAA to be deregistered as a charity, the pro-Israeli organisation is accused of trying to tarnish supporters of the Palestinians and anti-Zionists by labelling them anti-Semites.

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Thousands of petitioners have called for its charity status to be revoked. The decision to grant the CAA charity status, they say, is “outrageous”. They insist that “it provides no Public Benefit” and that its activities are not “remotely charitable”.

Describing the CAA as a “nakedly right-wing political Zionist organisation” lobbyists said they are horrified that a pro-Israeli organisation which is posing as a charity in the UK has been allowed to run such a politically divisive campaign against a democratically elected leader of a major political party.