Harry, 40, had received an "unequivocal apology" from NGN after "serious intrusion" by The Sun, including unlawful activities by private investigators working for the paper.
Hugh Grant has spoken out on Prince Harry's settlement
In April, the High Court heard that Hollywood star Grant had settled his case against NGN because of the risk of a £10 million legal bill if his case went to trial.
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British actor Hugh, who is part of the Hacked Off campaign group, told BBC Radio 4's Today programme: "Well, obviously, in light of these findings, we think that the CPS and the police should launch a new criminal investigation into this.
"And that was, as I say, the aim of Prince Harry's case, as I understand it, and certainly was my original aim in my case. And also, quite clearly now there should be Leveson Two.
Prince Harry's legal battle was just one of several ongoing disputes
"This is something that was repeatedly promised by the Labour Party in opposition to victims of press abuse over and over again, and now it suddenly seems to have disappeared from their priority list now that they’re in Government."
Many others had previously settled their claims against NGN, including actress Sienna Miller, ex-footballer Paul Gascoigne, comic Catherine Tate and Spice Girl star Melanie Chisholm.
WATCH: Prince Harry releases statement after huge win
Hugh settled a High Court claim against the publisher of The Sun after being advised he risked being liable for a £10 million legal bill if his case went to trial.
On Wednesday, the Duke settled his case against the publisher of The Sun. Harry alleged he was targeted by journalists and private investigators working for News Group Newspapers (NGN), which also published the now-defunct News Of The World.
LISTEN: Why Harry's legal deal is so extraordinary
In a statement outside the London court, Harry's barrister David Sherborne said NGN had spent "more than a billion pounds in payouts and in legal costs" in order to "prevent the full picture from coming out".
He also said: "In a monumental victory today, News UK have admitted that The Sun, the flagship title for Rupert Murdoch’s UK media empire, has indeed engaged in illegal practices.
"This represents a vindication for the hundreds of other claimants who were strong-armed into settling, without being able to get to the truth of what was done to them."
Buckingham Palace trigger police enquiry alleging News of the World's story on Prince William's knee injury could only have been attained through phone hacking.
January 2007
News of the World private investigator Glenn Mulcaire and royal editor Clive Goodman are sentenced to six and four months respectively for hacking the phones of royal aides. Goodman subsequently admits hacking William's phone 35 times and Princess Kate's over 150 times, but parent company News Corp maintains the pair were rogue employees.
January 2011
Police reopen the investigation after News of the World comes forward with "significant new information".
April 2011
News of the World admits liability for the phone hacking and pays actress Sienna Miller £100,000 in a related settlement. A slew of settlements with various famous people follow.
July 2011
The Guardian alleges News of the Worldhacked the phone of 13-year-old murder victim Milly Dowler during the police search for her, prompting mass outrage and the closure by Rupert Murdoch of News of the World.
November 2012
British Prime Minister David Cameron instituted the Leveson inquiry into media ethics, which would go on to recommend the creation of an independent press watchdog backed by the government. To date, not all the recommendations have been implemented.
October 2013
Former News of the World editors Andy Coulson and Rebekah Brooks are the most prominent defendants to go on trial at the Old Bailey on charges of phone hacking and making illegal payments to officials. The trial lasted eight months and resulted in Coulson being sentenced to 18 months in prison but the acquittal of Brooks.
December 2015
England's chief prosecutor says no more criminal cases will be brought against Murdoch's News Group and rival Mirror Group Newspapers.
2019
Prince Harry launches lawsuits against Murdoch's News Group Newsletters (NGN), the Mirror Group and Daily Mail publisher Associated Newspapers, claiming stories about his schooldays, teenage japes and former relationships were obtained illegally.
February 2021
Meghan Markle wins invasion of privacy lawsuit againstAssociated Newspapers over the publication of a letter she wrote to her estranged father in 2018.
June 2023
In his case against Mirror Group, Prince Harry became the first member of the British royal family since Prince Albert Edward (who would become King Edward VII) in 1891 to appear as a witness in court.
December 2023
Harry wins his case against Mirror Group but later says: "Our mission continues."
January 2025
Prince Harry's five-year-lawsuit against The Sun is over before it begins as the Duke, alongside fellow litigant Lord Tom Watson, reaches a shock settlement with publisher NGN agreeing to pay "substantial damages".
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