The Duke of Sussex, Baroness Doreen Lawrence and Sir Elton John are “delighted” after a High Court judge allowed their claims against the publisher of the Daily Mail to continue.

The three are among a group of high-profile individuals – including David Furnish, Sadie Frost, Liz Hurley and Sir Simon Hughes – who are bringing legal action against Associated Newspapers Limited (ANL).

They have accused the publisher of allegedly carrying out or commissioning unlawful activities such as hiring private investigators to place listening devices inside cars, “blagging” private records and accessing and recording private phone conversations.

At a hearing in March, ANL, which firmly denies the allegations, asked a judge to rule in its favour without a trial, arguing the legal challenges against it were brought “far too late”.

However, in a ruling on Friday, Mr Justice Nicklin said ANL had “not been able to deliver a ‘knockout blow’ to the claims of any of these claimants” and that the cases could continue.

In a statement issued by the law firm Hamlins on their behalf, the seven people in the claim said they were “delighted with today’s decision which allows our claims over serious criminal activity and gross breaches of privacy by the Mail titles to proceed to trial”.

The statement continued: “The High Court has dismissed ‘without difficulty’ the attempt by Associated Newspapers, publisher of The Daily Mail, The Mail on Sunday and the Mail Online, to throw these cases out.

“Indeed, the judge found that each of our claims had a real prospect of showing there was concealment of unlawful acts by the Mail titles and that this could not have been discovered until recently.

“Our claims can now proceed to trial.

“As we have maintained since the outset, we bring our claims over the deplorable and illegal activities which took place over many years, including private investigators being hired to place secret listening devices inside our cars and homes, the tapping of our phone calls, corrupt payments to police for inside information, and the illegal accessing of our medical information from hospitals and financial information from banks.

“We intend to uncover the truth at trial and hold those responsible at Associated Newspapers fully accountable.”

The ruling was also welcomed by actor Hugh Grant, a board director of press reform campaign group Hacked Off.

He said: “The Daily Mail’s argument, that the claimants should have disbelieved the newspaper’s aggressive protestations of innocence and brought claims sooner, was absurd and doomed to fail.

“When I reported my suspicions that the Daily Mail had carried out illegal activities to the Leveson Inquiry in 2012, the editor Paul Dacre attacked my sworn evidence as ‘mendacious smears’.

“I am pleased that a judge will now decide whether similar allegations made by Prince Harry, Baroness Lawrence, Sir Elton John and others are also mendacious smears or whether the mendacity lies with the other side.”

In their own statement following the decision, ANL said they “look forward” to establishing in court that the group had made “lurid” claims including phone-hacking and burglaries for hire.

The publisher also welcomed the judge’s decision that unpublished ledgers given to the Leveson Inquiry into the practices and ethics of the British press could not be used without Governmental permission, calling it a “significant victory”.

The spokesperson said: “We welcome Mr Justice Nicklin’s decision that the information we and other newspapers supplied to the Leveson Inquiry under strict grounds of confidentiality remains subject to the Restriction Order imposed by Lord Justice Leveson.

“In a significant victory for justice and the Mail, the judge ruled that the information should not have been used by the claimants and must be struck out from the case.

“As Mr Justice Nicklin says in his judgment, this was an ‘abuse of process’ and if used, ‘it would bring the administration of justice into disrepute’.

“As we have always made unequivocally clear, the lurid claims made by Prince Harry and others of phone-hacking, landline-tapping, burglary and sticky-window microphones are simply preposterous and we look forward to establishing this in court in due course.

“We are grateful to the judge for the careful consideration he has given to our applications.”