News International is to apologise to a number of the victims, and is to set up a compensation fund for those directly affected, to deal with "justifiable claims efficiently", according to the BBC.
This is the first time that the newspaper and media conglomerate has admitted it was at fault.
News International said in a statement:
"Past behaviour at the News of the World in relation to voicemail interception is a matter of genuine regret. It is now apparent that our previous inquiries failed to uncover important evidence and we acknowledge our actions were not sufficiently robust."
Last week saw the arrest of two journalists with the News of the World newspaper, Ian Edmonson and Neville Thurlbeck; the first arrests in five years, after the initial conviction of two prior journalists, Clive Goodman and Glenn Mulcaire.
Lord Prescott, former deputy prime minister for the British government during the time Labour was in office between 1997 and 2007, claimed that the Scotland Yard had informed him that "all newspapers were implicated" in the hacking of mobile phones.
The incumbent Conservative government was implicated when Andy Coulson, then press and communications director to the Prime Minister, was questioned by Scotland Yard investigating officers regarding his time at the newspaper, and was forced to resign.