The Duke of Sussex’s privacy claim against the publisher of the Daily Mail is rejected “in its entirety”, brought “far too late”, and should be thrown out by a judge, the High Court has been told.

Associated Newspapers Limited (ANL) says legal challenges brought by a number of high-profile individuals, including Sir Elton John and Baroness Doreen Lawrence of Clarendon, have “no real prospects of succeeding” at a trial.

The publisher’s lawyers argued at the High Court in London on Wednesday that the cases should be dismissed or a judgment made in its favour without a trial.

But the legal team for Harry and others say ANL’s bid is “hopeless, plainly inappropriate and suggestive of a tactical gamble” to avoid a full trial.

Harry, who did not return to court for the third day of an ongoing preliminary hearing, alleges that he was the victim of unlawful or illegal information gathering and says he is concerned by the “unchecked power, influence and criminality” of ANL.

The duke and others, including actresses Liz Hurley and Sadie Frost and ex-Liberal Democrat MP Sir Simon Hughes, allege that ANL hired private investigators to place listening devices inside cars, “blag” private records, and access and record private phone conversations over a period starting from 1993.

Six of those bringing cases against the publisher have referred to alleged confessions by private investigator Gavin Burrows in their claims, but ANL has highlighted a later witness statement from Mr Burrows in which he denies being commissioned by its newspapers to conduct unlawful information gathering.

Both of Mr Burrows’ statements have now been released to journalists this week.

Adrian Beltrami KC, for the publisher, told the court on Wednesday: “The claims are rejected by the defendant in their entirety as are the unfounded allegations that are repeatedly made that the defendant either misled the Leveson Inquiry or concealed evidence from the Leveson Inquiry.”

He said the various claims were “barred” under a legal period of limitation, adding: “Whatever claims the claimants had or may have had have been brought far too late.”

In written arguments, Mr Beltrami said that the privacy claims against it could have been brought before October 2016 and that “almost the entirety” of cases could with “reasonable diligence” have been discovered before that date.

The barrister added that many of those bringing the claims had brought legal action against other newspaper groups and had hired lawyers involved in the Leveson Inquiry into press standards and phone hacking litigation as well as a “research team”.

“It is inconceivable that what is claimed to be the key new information leading to each claimant realising they had a claim arrived unbidden in the past couple of years,” Mr Beltrami said.

“It must have been the product of a process, probably over a number of years.”

He concluded that “the court should not hesitate to dismiss these stale claims at an early stage, thereby avoiding what would otherwise be a considerable waste of time, costs and the court’s resources”.

David Sherborne, representing the group bringing the legal action, said in written arguments that they “heavily resisted” ANL’s bid to have their cases dismissed.

He said the evidence so far over ANL’s alleged unlawful information gathering “appears compelling”, but that this should be decided at a trial.

Mr Sherborne questioned how the group could have discovered they had potential cases where “as a result of the defendant’s deliberate concealment and the intentionally covert nature of the underlying acts themselves, the vast majority of the evidence is necessarily in the defendant’s own possession”.

The duke and others “did not discover it until recently,” he added.

ANL has previously argued that parts of the cases brought against it rely on documents that were provided by the company to the Leveson Inquiry in 2011 and 2012 with the understanding that they were confidential.

The publisher said these documents are subject to publication restriction orders over their use, and that lawyers for Harry and others are in breach of these by relying on them without first applying for their disclosure.

Mr Sherborne said the material is not covered by the inquiry’s restriction orders.

In a witness statement released on Tuesday, Harry has alleged that journalists at ANL “are criminals with journalistic powers which should concern every single one of us”.

ANL has branded his allegations as “untrue, inflammatory and deeply offensive”, accusing him of being “obsessed” with its newspapers.

Baroness Lawrence, the mother of murdered teenager Stephen Lawrence, claims to have been the victim of the illegal interception of her voicemails, monitoring of her bank accounts and “corrupt payments to serving Metropolitan Police Service police officers, including on the Stephen Lawrence murder investigations, for confidential information”.

Sir Elton and his husband David Furnish have alleged the landline phone of their Windsor home was tapped by investigators on ANL’s behalf and that the birth certificate of their first child was unlawfully obtained by the publisher.

Mr Furnish and Ms Frost continued to attend court on Wednesday, following visits by Harry, Sir Elton and Baroness Lawrence this week.

The hearing before Mr Justice Nicklin is due to conclude on Thursday, with a ruling expected at a later date.