News International, Rupert Murdoch's company which owns the News of the World, is under pressure following its admission that its journalists had hacked into the mobile phones of at least eight public figures.
New International has offered compensation to victims, who include actor Sienna Miller, former soccer player turned broadcaster Andy Gray and former British deputy prime minister John Prescott.
Deputy Leader of the Liberal Democrats Simon Hughes has said those responsible for having committed a criminal offence should be prosecuted.
News International said yesterday it had instructed lawyers to set up a compensation scheme to deal with ‘justifiable claims’ and said ‘past behaviour’ at the newspaper was ‘a matter of genuine regret’.
Mark Lewis, who is acting for a number of personalities who claimed their phones were hacked, said the final compensation bill could easily run into millions of pounds.
The announcement came after a number of well-known figures took High Court action over allegations of phone-hacking.
The controversy has been a source of continuing embarrassment for News International at a time when its parent group, News Corporation, has been seeking to take full control of BSkyB.
Yesterday, Mr Prescott reiterated his call that the controversial takeover should be delayed until police have completed their inquiry into the allegations.
Earlier this week, detectives investigating the allegations arrested the paper's chief reporter and its former head of news.
Neville Thurlbeck, 50, and Ian Edmondson, 42, were held by Scotland Yard detectives on Tuesday when they voluntarily attended separate police stations in south-west London.
Officers questioned the pair on suspicion of conspiring to intercept communications and unlawfully intercepting voicemail messages.
The men were later released on police bail to return in September.