Harry, Elton John, his husband David Furnish, campaigner Doreen Lawrence, politician Simon Hughes and actresses Sadie Frost and Liz Hurley are all taking action against Associated Newspapers Limited (ANL).
The group claims that the publisher carried out or commissioned unlawful activities such as hiring private investigators to place listening devices inside cars, "blagging" private records and accessing private phone conversations.
ANL, which also publishes the Mail on Sunday, has strongly denied wrongdoing.
The trial before Justice Nicklin will be heard at the Royal Courts of Justice from 10.30am on Monday and is due to last nine weeks.
The group started their legal cases against ANL in 2022, with documents setting out the claims naming dozens of journalists, including some national newspaper editors.
In 2023, ANL failed to have the cases thrown out before a trial on the basis that they were "time-barred", or brought too late.
In written submissions for the hearing in May that year, Adrian Beltrami KC, for ANL, said that the legal actions were "stale".
He also said that the individuals had to prove they did not know earlier, or could not have discovered earlier, that they might have had a claim against it for alleged misuse of their private information.
Barrister David Sherborne, for the group, told the hearing that the unlawful acts in the claim include illegally intercepting voicemail messages, listening to live landline calls and obtaining medical records.
"They range through a period from 1993 to 2011, even continuing beyond until 2018," he said,
Justice Nicklin dismissed ANL's bid to have the claims dismissed in November 2023, ruling that the publisher had not delivered a "knockout blow" to the claims.
He concluded that each of the group had a "real prospect" of demonstrating that ANL concealed "relevant facts" that would have allowed them to bring a claim against the publisher earlier.
There have been several preliminary hearings in the claim, including one in November 2024 that heard that Lady Lawrence was "alerted" to a potential legal claim by a text from Harry.
Harry has previously brought legal action against other newspaper publishers over allegations of unlawful information gathering.
He was awarded by a judge stg140,600 ($A280,300) in damages from Mirror Group Newspapers in 2023, and settled a claim against News Group Newspapers, the publisher of the Sun and the now-defunct News Of The World.
