Four people mounting a fresh High Court Brexit challenge say they have safety fears and want to remain anonymous.
A judge on Tuesday said the four had a strong case and made an order barring journalists from revealing their names in reports on the case.
But Mr Justice Cranston gave media organisations permission to challenge his order after a reporter raised concerns about the principle of open justice being undermined.
Lawyers representing the four outlined detail of the case, and arguments for anonymity, at a preliminary High Court hearing in London.
They indicated that the four wanted a judge to analyse the Government's EU withdrawal plans.
Lawyers said a claim had been launched against David Davis, Secretary of State for Exiting the European Union, but no date had been fixed for a final hearing.
The four were referred to by the letters W,L, T and B in case listings.
Ministers are waiting for Supreme Court justices to rule on a Brexit challenge spearheaded by businesswoman Gina Miller.
Government lawyers appealed after judges at a High Court hearing ruled that Parliament must have the final say on invoking Article 50, which formally begins the withdrawal process.
Lawyers for the four people behind the latest litigation said the fresh claim would centre on Britain's links with the European Economic Area.
They said the four would argue that parliamentary approval was needed to quit the EEA.
Lawyers said the four would raise issues relating to people of mixed nationality living in Britain who might be left in "limbo" as a result of Brexit.
They said Ms Miller, an investment fund manager, had been threatened, and evidence suggested that the four people could also be at risk.
Mr Justice Cranston said lawyers for the four had mounted a "very strong case" for anonymity.
But a reporter covering the hearing said barring journalists from identifying the four would undermine the open justice principle, and suggested editors should be given the chance to study anonymity arguments in detail before deciding whether they wanted to mount a challenge.
The judge said he was concerned that media organisations had not been properly notified of the application for anonymity, and editors should be given the opportunity to challenge it.
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