These included hacking mobile phone messages, bugging calls, getting private information such as medical records by deception or "blagging", and "commissioning the breaking and entry into private property", their lawyer David Sherborne said.
Harry, who flew in from his California home, sat just feet away from reporters, watching intently and taking notes.
Elton John, Furnish, Frost and another claimant, Doreen Lawrence, mother of Black teenager Stephen Lawrence who was murdered in a 1993 racist attack, were also in court on Monday.
Harry hugged Lawrence at the end of the day's hearing and chatted to her and Furnish, and gave a thumbs up to crowds outside as he left court.
[1/8] Britain's Prince Harry, Duke of Sussex, arrives at the High Court in London, Britain March 27, 2023.