Great British Bake Off presenter Noel Fielding and Ryan Giggs' brother Rhodri are among the latest people to accept "substantial damages" over phone-hacking by tabloid journalists.
News Group Newspapers (NGN) apologised for "distress" caused by the illegal interception of voicemails.
NGN's paper, News of the World, was closed down in 2011 after years of phone-hacking came to light.
Hundreds of celebrities and members of the public have since won compensation.
Mr Fielding's solicitor, Alex Cochrane, told a court hearing in London on Thursday that the Mighty Boosh and Never Mind The Buzzcocks star had identified a number of articles published between 2006 and 2010 which he claimed contained his private information and were "suspicious".
"During this time, Mr Fielding used his voicemail extensively and he would regularly receive and leave voicemail messages for his family and close friends," Mr Cochrane told the court.
"It was alleged that the publication of the articles generated distrust which impacted his relationships and caused him considerable distress."
Other victims who settled their claims at the hearing are:
- David and Victoria Beckham's former personal assistant Rebecca Loos
- Actress Sadie Frost's mother Mary Davidson and sister Jane Davidson - both of whom worked as a nanny for supermodel Kate Moss
- TV producer Bradley Adams, who was a business associate of Frost and her then-husband, actor Jude Law
- Artist Zoe Grace, who was friends with Moss, Frost and Law
- Sarah Vincent, the ex-wife of comedian Vic Reeves
- Actress Roxanne Pallett, who played Jo Stiles in Emmerdale
- The wife and manager of actor Ricky Tomlinson, Rita Tomlinson
- Former footballer Ally McCoist
- Guitarist Patrick Walden, who was a member of Pete Doherty's band Babyshambles
- Actor Chris Bisson, who currently plays Jai Sharma in Emmerdale
Solicitor Callum Galbraith, whose firm Hamlins represented everyone at Thursday's hearing apart from Mr Bisson, said: "Getting as full an understanding of NGN's unlawful acts is critical to many of our clients, but equally many want a full and proper apology acknowledging the considerable distress and lasting damage caused. These public apologies achieve that."
NGN's barrister, Ben Silverstone, said the defendant offered its "sincere apologies" to the claimants "for the distress caused to [them] by the invasion of [their] privacy by individuals working for or on behalf of the News of the World.
"Such activity should never have taken place," he added.
News of the World, which was owned by Rupert Murdoch, obtained stories by listening in to the private voicemail messages of celebrities and even the murdered teenager Milly Dowler.
Those who have already settled their cases for undisclosed sums include singer Sir Elton John and actress Elizabeth Hurley.
Combined with legal costs, the bill for NGN - which is also the publisher of the Sun newspaper - has run into hundreds of millions of pounds.
The publisher has never admitted liability in relation to alleged phone-hacking at the Sun.
There are about 50 phone-hacking claims against NGN remaining in the latest round of litigation, with a trial for some lead cases set to go ahead in November.
In the past few years, several trial dates have been set only for claims to be settled at the last minute.
Lawyers representing alleged phone-hacking victims say that, aside from the cases already in the system, many more could yet be brought before the courts.