Norman Thomas, of Platform Films, said claims that the film was antisemitic were “a total smear” and had no foundation “whatsoever”.
Glastonbury previously said that although the film, titled Oh, Jeremy Corbyn: The Big Lie, had been booked “in good faith”, it had decided that it was not appropriate to screen.
It came after the Board of Deputies of British Jews (BDBJ) expressed “deep concern” over the film and said it was “profoundly sinister” for Glastonbury to be providing it with a platform.
In a statement shared with the PA news agency Mr Thomas said the cancellation had been caused by “vicious outside pressure”.
“An outside pressure group has declared war on our film,” he said.
“They wrote to the festival’s sponsors… and whipped up huge storm of complaints about the film claiming, without any foundation whatsoever, that the film is antisemitic.”
He continued: “The claim that the film is antisemitic is a total smear.
“The festival organisers even had a lawyer examine the film who pronounced it totally devoid of antisemitism.”
According to Platform Films, the documentary claims Mr Corbyn was a victim of a “concerted smear campaign”, that current Labour leader Sir Keir Starmer played a “deceptive spy cop” role in Mr Corbyn’s shadow cabinet and that Sir Keir is now “waging a witch-hunt in the party”.
It was due to be shown on June 25 at Glastonbury’s Pilton Palais cinema and described, according to the BDBJ, as “the banned Corbyn documentary”.
“This has gone on long enough.
“Journalists, who know very well what’s going on, have to stand up and call this out for what it is: rank censorship,” Mr Thomas said.
“The problem is, if they do, they fear being accused of antisemitism.
“But if enough of us stand together the accusation won’t stick and this madness will end.”
A statement attributed to Glastonbury said: “Although we believe that the Pilton Palais booked this film in good faith, in the hope of provoking political debate, it’s become clear that it is not appropriate for us to screen it at the festival.
“Glastonbury is about unity and not division, and we stand against all forms of discrimination.”
The festival’s decision came following a letter sent by BDBJ president Marie van der Zyl to Glastonbury organisers Michael and Emily Eavis.
“This film, we understand, seeks to suggest that organisations such as the Board of Deputies of British Jews, of which I am the president, somehow helped to ‘orchestrate’ Jeremy Corbyn’s downfall as Labour Party leader,” Ms van der Zyl wrote.
Adding that the initial decision to show the film was “worrying” her letter continued: “Your festival is one of the most successful festivals in the UK.
“It seems profoundly sinister for it to be providing a platform to a film which clearly seeks to indoctrinate people into believing a conspiracy theory effectively aimed at Jewish organisations.
“We would request that you not allow your festival to be hijacked by those seeking to promote hatred with no basis in fact, in the same way as we would hope that your festival would not screen films seeking to promote other conspiracy theories, such as anti-vaccination, 9/11 truthers or chemtrails.”
The BDBJ later said it was pleased the film would no longer be shown at the festival.
“We are pleased that in the wake of a letter we sent earlier today, @glastonbury have announced the cancellation of the screening of this film,” the organisation wrote on Twitter.
“Hateful conspiracy theories should have no place in our society.”