The businessman Arron Banks and the unofficial Brexit campaign Leave.EU have issued a legal threat against streaming giant Netflix in relation to The Great Hack, a new documentary about the Cambridge Analytica scandal and the abuse of personal data.

The threat comes as press freedom campaigners and charity groups warn the government in an open letter that UK courts are being used to “intimidate and silence” journalists working in the public interest.

In a joint letter to key cabinet members, they call for new legislation to stop “vexatious lawsuits”, highlighting one filed last week by Banks against campaigning journalist Carole Cadwalladr.

Award-winning reports by Cadwalladr, a freelance journalist who works for the Observer, have led to multiple investigations by regulators, and a $5bn fine for Facebook.

“The legal claim against Ms Cadwalladr, issued on 12 July by lawyers acting for Arron Banks, is another example of a wealthy individual appearing to abuse the law in an attempt to silence a journalist and distract from these issues being discussed by politicians, the media and the public at a critical time in the life of our democracy,” the letter says.

Banks had not seen The Great Hack, which comes out on general release on Netflix this week, when he instructed lawyers over the documentary.

London law firm Kingsley Napley, acting on behalf of Banks, his company Eldon Insurance, and Leave.EU, said in a letter on 16 July that their clients were concerned it would include “false and defamatory allegations” about their clients made by Cadwalladr and others.

The Observer understands they demanded a right to see any allegations made in the film, and be given a chance to respond, by Wednesday 17 July. The lawyers warned Netflix they would rely on any failure to respond, or failure to meet their demands, in any future legal proceedings they considered necessary or appropriate.

The Great Hack’s co-director Karim Amer said: “We have received a letter from Arron Banks’s solicitors, which we have responded to, making clear that we stand by the contents of the film and will vigorously defend against any claim. We find it ridiculous that Arron Banks and his solicitors would issue such a letter without having seen the actual film.

“We would invite Mr Banks to watch the film when it premieres worldwide on Netflix on 24 July.” He added that Banks would be welcome at a London screening at the ICA that day.

The Observer’s editor, Paul Webster, criticised the legal action against Cadwalladr. “Throughout her investigations she has been the target of a relentless campaign of smears and vilification by some of the subjects of her inquiries,” he said.

“The latest legal threats are a further attempt to smother vital investigative reporting.”

Banks said: “I’m a great supporter of a free media and press. Unfortunately, Brexit has caused a breakdown in usual journalistic standards.

“What we won’t tolerate is outright lying or misrepresentation of the facts … Carole Cadwalladr will have to stand up her wild claims in court and face the consequences or apologise,” he said. He did not comment on the letter sent to Netflix.

Press freedom campaigners who signed the joint letter to the UK government say they have noted a growing trend of wealthy individuals using lawsuits to silence or intimidate journalists.

How the Observer covered the Cambridge Analytica story in March 2018.

The 16 signatories included Webster, and the directors of leading media and artistic freedom groups the Committee to Protect Journalists, PEN, Index on Censorship, Reporters Sans Frontières ,campaign group Greenpeace, a law scholar and the family of murdered Maltese journalist Daphne Caruana Galizia.

In addition to Banks’s case against Cadwalladr, the letter also highlights legal threats to Galizia, who at the time of her death faced more than 40 civil lawsuits, many brought by UK-based firms.

Often the spectre of costly legal action can force a retraction or prevent a story being published; in other cases rich individuals may hope to silence critics with limited resources through the cost and time of a court case.

“One of the things we have become increasingly worried about was the use of legal threats to silence journalists, and especially the threat of expensive libel suits,” said Jodie Ginsberg, chief executive of Index on Censorship.

In the US there have long been concerns about lawsuits of this kind, which are known as “strategic litigation against public participation”, or “Slapp” cases. Several states have laws that stop these cases being brought to court.

Sometimes just the threat of legal action can kill a story. “Slapp lawsuits can be a very low-cost means of [subjects of negative reporting] getting what they want, because quite often they don’t even need to take anyone to court,” said Rebecca Vincent, UK director of Reporters Sans Frontières.

The organisation last year gave Cadwalladr its L’esprit de RSF award, and Vincent praised her for discussing the lawsuit publicly.

“I think she is very courageous about speaking out about this abusive defamation lawsuit that has been filed against her, because so often these cases remain hidden,” she said.

Cadwalladr has questioned why Banks chose to lodge a personal case against her rather than suing the outlets that published her work, or the Ted platform that hosted a speech at the heart of his case, which have resources to fight a long legal battle.

“Arron Banks is not suing Ted or the Guardian and Observer, though it is the extensive investigations that we have published and that have helped trigger several serious criminal investigations that has prompted this lawsuit,” she said.

“Instead, he has chosen to go after me as an individual in a clear attempt to intimidate and harass me. It’s extremely concerning that a millionaire can use the law in this way. This isn’t just an attack on me, it’s an attack on journalism.”

This year Britain has positioned itself as a world leader on media freedom, hosting a global conference, appointing barrister Amal Clooney as a special envoy on the issue, and promising to consider the impact on press freedom of any new legislation.

Ginsberg urged authorites to make good on those promises by cracking down on abuses within the country. “Given that the UK has made media freedom its major focus for 2019, one way it could take a lead is dealing with the big UK law firms who are helping the rich and powerful to stifle investigative journalism.”