The Guardian and other media organisations have won the right to report on a court hearing about whether an injunction protecting the identity of a celebrity couple should be lifted.

The court of appeal case, involving an allegation of a threesome, has raised the issue of whether injunctions restricting reporting can be enforced in the era of the internet.

The appeal by News Group Newspapers on behalf of the Sun on Sunday as to whether the injunction should be lifted is now being heard.

Details of the supposed affair, involving one of the couple and another couple, have already been widely reported in Scottish, US and other foreign newspapers, beyond the jurisdiction of the courts of England and Wales.

A court in London had originally granted the injunction, preventing identification of those involved, against the Sun on Sunday newspaper. Judges said that naming the celebrity couple could harm their children.

Gavin Millar QC, for News Group Newspapers, told the court of appeal on Friday that the interim injunction preventing publication should be lifted.

“We say that the events of the past 10 days make it unlikely that the claimant will succeed at getting a permanent injunction at trial,” Millar told the court.

But Desmond Browne QC, for the celebrity claimant who has only been identified by the initials PJS, accused sections of the press of whipping up hostility to the courts.

A retrospective claim for damages would deny the claimant “the only form of relief that is worth having”, Browne told the hearing.

“The media, and I refer particularly to … the defendants and publishers of the Mail, have sought to ridicule the granting of the injunction,” he said.

One paper had printed a cut-out template for readers to send to their MPs demanding that restrictions on reporting the “celebrity threesome” be lifted.

“Not all the secrecy had escaped,” Browne added. “There has been no mainstream publication in this jurisdiction [England and Wales] that directly infringes the order.”

He maintained that the accessibility of the information online was not the same as it being readily available.

“In this case the order is needed to prevent a media storm which would be devastating for the claimant and the children.”

Guy Vassall-Adams QC, representing the Guardian and other media organisations, had argued in his written submission that the anonymised issues in the case should be reportable in the interest of open justice.