Media reports suggest that News Group Newspapers, a subsidiary of the Rupert Murdoch-owned News International, will today agree deals with 19 phone hacking victims in advance of a planned trial next week.
They are thought to include Tony Blair's former spin doctor Alastair Campbell, Chelsea footballer Ashley Cole actor Jude Law and ex-England footballer Paul Gascoigne.
Gascoigne's best friend Jimmy 'five bellies' Gardener is also in line for a payout, along with George Best's agent Phil Hughes and Elliot Morley, the former minister who was jailed for cheating his expenses.
This will bring the number of cases settled to around 40, although it is thought that more than 20 cases are still to be concluded.
Details of the settlements are expected to be confirmed later today during a pre-trial hearing on the phone hacking claims.
It is unclear how much the pay-outs with cost Murdoch's News Corporation, which has already shelled out millions in compensation to victims, including a £3m settlement with the family of murdered schoolgirl Milly Dowler last year.
News International set up a £20m compensation scheme in April 2011 as part of plans to settle the hacking claims before they reached the high court.
> News International settles hacking claims with Ulrika Jonsson, others
He said: "When the now defunct News of the World investigated and published stories about people, including people high up in government as well as other people in the public eye, it systematically ignored any privacy rights and interests they might have, and knew no limits in what it was prepared to do to get a story. It had a distorted idea of the 'public interest', justifying its behaviour like a tyrannical father."
Bindmans, the law firm representing a number of hacking victims, said that many people have been "severely affected" by News Group's "cavalier approach to private information and the law".
"The claimants now have some clarity about what happened to them in the years between 2000 and 2005 and satisfaction that justice has finally been done," said Bindmans' Tamsin Allen in a statement reported by The Guardian.
"Lives have been severely affected by this cavalier approach to private information and the law. News Group's misguided decision to defend claims aggressively made matters worse.
"News Group have finally started to see sense and agreed to apologise and to pay compensation and costs in the majority of the remaining claims."
Allan also said that the ongoing Leveson inquiry into press ethics and standards will "reveal to the public the full extent of the perversion of good journalistic standards at the News of the World during the phone hacking years".
Yesterday at the Royal Court of Justice inquiry, Heat magazine editor Lucie Cave defended the art of the celebrity exposé, saying that it can be in the public interest to reveal the actions of hypocritical celebrities who claim to be role models.