News International cannot rule out the possibility that News of the World staff continued hacking phones even after one of the paper's reporters was jailed for the illegal practice, the Leveson Inquiry heard today.
But the publisher questioned claims that as many as 28 of the Sunday tabloid's journalists commissioned private investigator Glenn Mulcaire to intercept voicemail messages.
It emerged today that the family of murdered schoolgirl Milly Dowler, whose phone was hacked by the News of the World after she vanished in 2002, will be the first witnesses to give evidence to the inquiry into press standards next week.
A total of 21 people who have complained about press intrusion - including actor Hugh Grant, the parents of missing Madeleine McCann and former Formula 1 boss Max Mosley - are expected to appear before the hearings.
Former information commissioner Richard Thomas will tell the inquiry on December 1 about his investigation into the unlawful trade in confidential personal information.
Ex-Number 10 communications director Alastair Campbell will also give evidence. He is expected to focus on the relationship between national newspapers and politicians.
Rhodri Davies QC, counsel for News International, told the inquiry today that "lessons were learned" when News of the World royal editor, Clive Goodman, was jailed in 2007 for hacking royal aides' phones.
But he admitted: "I am not going to give any guarantees that there was no phone hacking by or for the News of the World after 2007."
Police believe that illegal voicemail interception at News International had begun by 2002 and continued until at least 2009, the inquiry sitting at the Royal Courts of Justice in London has heard.
Mulcaire's notebooks, which were seized by detectives in 2006, suggest that at least 27 of the publisher's employees other than Goodman commissioned him to hack phones, the hearing was told.
Mr Davies queried this figure and asked for it to be checked again.
The barrister said News International had never seen the full set of 11,000 pages of Mulcaire's notes held by police, but accepted they included the names of Goodman and four other News of the World journalists referred to as A, B, C and D.
He went on: "We also know that the police believe there are a number of others which can be correlated to News of the World journalists.
"We do not know the names and we are not in a position to assess that, one way or another. Nor do we know how many, but what we understand is that it certainly does not add up to 27."
News International disputes claims that Mulcaire's notebooks show that The Sun newspaper commissioned him to hack actor Jude Law's phone, the inquiry heard.
Mr Davies issued a fresh apology for the News of the World phone hacking scandal, which he said was "wrong, shameful and should never have happened".
The lawyer said News International now accepted that the illegal interception of voicemails was not carried out by a single "rogue reporter", and that it was not properly investigated until police launched a new inquiry in January.
He also described the commissioning of a private detective to spy on lawyers for phone hacking victims and MPs looking into the scandal as "wholly unacceptable".
Mr Davies stressed that newspapers were already constrained by the UK's civil and criminal laws, and that new legislation was passed over the past 15 years to provide protection in areas where there was concern over the media's behaviour.
He made a plea to inquiry chairman Lord Justice Leveson for the press not to be "over-regulated" but added: "It's not a plea for it to be above the law."
Meanwhile, the publisher of the Daily Mail issued a robust defence of its journalists and insisted it had no evidence linking staff to phone hacking.
Jonathan Caplan QC, counsel for Associated Newspapers, said the company's employees did not bribe police officers and condemned the "shameful" practice of tapping into the voicemails of victims of crime.
Prime Minister David Cameron set up the Leveson Inquiry in July in response to the revelations that the News of the World hacked 13-year-old Milly's phone.
The first part, which formally began on Monday, is looking at the culture, practices and ethics of the press in general.
The second part, examining the extent of unlawful activities by journalists, will not begin until detectives have completed their work and any prosecutions have concluded.