Prince Harry and five other prominent figures have launched a legal challenge against a judge’s verdict in their unsuccessful claims against the Daily Mail publisher Associated Newspapers.

Harry, Doreen Lawrence, the mother of the murdered black teenager Stephen Lawrence, the singer Elton John and his husband, David Furnish, and the actors Elizabeth Hurley and Sadie Frost faced a legal bill of more than £50m after losing their case claiming that Mail journalists used unlawful methods to source stories.

In an unequivocal ruling in July, Mr Justice Nicklin dismissed their case, stating that the claimants had not proved that any information had been obtained unlawfully.

His 436-page written verdict, following an 11-week trial, said it could not be inferred that a story had been obtained unlawfully if there remained a legitimate and realistic legal way in which it could have been sourced.

In a statement issued on Friday, a spokesperson for Harry and his five fellow claimants said: “We confirm that the claimants have today filed applications with the court of appeal for permission to appeal the judgments of Mr Justice Nicklin in respect of his dismissal of their claims and the indemnity costs order.

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

Court staff confirmed on Friday that a bid to appeal against the rulings had been filed at the court of appeal.

Barristers for the claimants had alleged at trial that private investigators, freelance journalists and staff at Associated Newspapers had carried out acts including voicemail interception, landline tapping and obtaining information by deception – also known as “blagging”.

But lawyers for the publisher said Daily Mail and Mail on Sunday journalists provided a “compelling account of a pattern of legitimate sourcing of articles”, including friends and “leaky” social circles, press officers and spokespeople, as well as previous reporting, freelance journalists and stories from other newspapers and news agencies.

Associated’s legal team described the claims as “lurid” and “preposterous”.

After the verdict the former Mail editor Paul Dacre said the case was a “conspiracy” orchestrated by press regulation campaigners to “destroy a paper”.

Harry and Lawrence said the verdict was a “complete and obvious whitewash”. They added: “When the court says there is not sufficient evidence of wrongdoing … then one does wonder how justice was ever going to be achieved.”

In August, Nicklin ruled that the claimants had to pay £9,544,355 within seven days as an initial contribution to the publisher’s costs before further hearings to determine the total sum.