The Duke of Sussex and five other high-profile figures who lost a privacy case against the publisher of the Daily Mail and Mail on Sunday are seeking to challenge the High Court ruling.

Prince Harry, singer Sir Elton John and actress Elizabeth Hurley were among the group facing paying joint legal costs of up to £34.5m after the court ruled in July they had failed to prove the allegations of unlawful information gathering.

Associated Newspapers Limited strongly denied the claims, which were heard at an 11-week trial in London that ended with judge Mr Justice Nicklin dismissing all the allegations.

At the time, a spokesperson for the publisher described the judgement as an “overwhelming victory for the Daily Mail and its journalists”.

The prince testified in person during the civil hearing and claimed the details that appeared in 14 articles about him “plainly” proved journalists were listening in to phone calls – but a High Court judge said he had failed to prove that.

On Friday, a spokesperson for Prince Harry, Hurley, Sir Elton, his husband David Furnish, actress Sadie Frost and political campaigner Baroness Lawrence said the claimants had filed applications with the Court of Appeal applying for permission to challenge the judgements.

The statement said the planned appeal was both on Mr Justice Nicklin’s dismissal of their claims and a subsequent indemnity costs order.

The spokesperson said: “The claimants respectfully disagree with those unprecedented decisions, which they consider to be legally and factually flawed.”

In August, a month on from his judgement, Mr Justice Nicklin ruled that the case was a rare one in which the claimants should have to pay far in excess of the costs that had been agreed before the trial.

He also ordered at that time the claimants should make an initial payment of £9.54m while the final total was calculated.

The statement from the group’s joint spokesperson did not make any reference to Liberal Democrat politician Sir Simon Hughes who was part of the action. The BBC has contacted Sir Simon to establish whether he is joining the appeal.

After the costs ruling, he told the BBC he was “disappointed” and would take “the time necessary to consider both the substantive and the costs judgment and whether to pursue appeals against decisions in either judgment or both”.

The trial saw many current and former Mail and Mail on Sunday journalists and executives giving evidence denying accusations of illegal activity that was put to them by lawyers representing the prince and his fellow claimants.

Lawyers for the publisher said in court that the journalists had provided a “compelling account of a pattern of legitimate sourcing of articles”, including using information provided by friends and “leaky” social circles surrounding those they had written about.

In a civil case such as this, the legal convention is that the losing party must reimburse “reasonable” legal fees incurred by the other side. They also have to settle their own legal costs.