The Duke of Sussex and five fellow claimants have applied for permission to appeal against both the dismissal of their privacy case against the Daily Mail’s publisher and a costs ruling, with joint legal costs potentially reaching £34.5m.

The applications challenge two decisions: Mr Justice Nicklin’s finding in July that unlawful information gathering had not been proved, and his subsequent order requiring the claimants to pay costs far above those agreed before the trial.

A spokesperson confirmed on Friday that Harry, Sir Elton John, his husband David Furnish, actresses Elizabeth Hurley and Sadie Frost, and political campaigner Baroness Lawrence had filed applications with the Court of Appeal.

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

Associated Newspapers Limited, which publishes the Daily Mail and Mail on Sunday, strongly denied the allegations. Mr Justice Nicklin dismissed them all following an 11-week civil trial in London. At the time, a publisher spokesperson called the judgement an “overwhelming victory for the Daily Mail and its journalists”.

The dispute centred on how journalists obtained private information. Harry gave evidence in person, arguing that details in 14 articles about him “plainly” proved journalists had listened to phone calls. The judge found that he had failed to prove that claim.

Current and former journalists and executives from both newspapers gave evidence denying illegal activity. The publisher’s lawyers argued that they had provided a “compelling account of a pattern of legitimate sourcing of articles”, including information from friends and “leaky” social circles around the claimants.

The financial consequences extend beyond the usual obligation in civil litigation for the losing side to reimburse the other party’s reasonable legal fees while meeting its own. In August, Mr Justice Nicklin found this was a rare case warranting substantially higher costs and made an indemnity costs order. He ordered an initial payment of £9.54m while the final total was calculated.

Sir Simon Hughes, the Liberal Democrat politician who was also part of the original action, was not named in Friday’s statement. Whether he is joining the appeal remains unclear. After the costs ruling, he said he was disappointed and would take time to consider challenging either or both judgements.

The six applicants are seeking permission to appeal; their applications do not themselves reopen the trial or overturn either ruling.