Lawyer Charlotte Harris, who represents several of the celebrities involved, said up to 7,000 people may have had their mobile phone voicemail intercepted.
The claim came as the News of the World publicly apologised to victims in the latest edition of the newspaper, saying: “Here today, we publicly and unreservedly apologise to all such individuals. What happened to them should not have happened. It was and remains unacceptable.”
Ms Harris, whose clients include football agent Sky Andrew, said the position for him was the same as that of publicist Nicola Phillips and actress Sienna Miller, who have said that they would not accept a settlement from the newspaper until they had received full disclosure.
She said: “What we have at the moment is an apology and an admission, having been working on this for a very long time. We haven’t even got near the truth yet.”
Discussing the number of phones which could have been hacked into, Ms Harris said: “If you consider that if you hack into one person’s phone, you have access to everyone who has left a message for them. And then, if you go into the person who has left a message, you get all of theirs.
“You have got to be running into several thousand, just from that methodology. To put a figure on it, it is certainly not a handful – maybe 4,000, 6,000, 7,000 – a huge amount of people.”
There has been widespread condemnation of the phone-hacking, with Cabinet Minister Danny Alexander describing it as “outrageous”.
He said it was a “very serious scandal” and that court cases and the police investigation “must go forward”.
Shadow Welsh secretary Peter Hain also stressed the importance of the police investigation, and added: “Who knows what they were up to really? This is a really serious media scandal.”
Mayor of London Boris Johnson has called for all newspaper editors to declare any phone hacking by their own staff, saying there needed to be “a general truth and reconciliation commission”.
Ms Miller’s solicitor has said the actress would do everything possible to hold to account those responsible for the “outrageous violations of her privacy”. She has not accepted any offer of settlement and will “consider her next steps” once she has had information and disclosure from the News of the World, Mark Thomson said.
It is understood that along with Ms Miller, the company has issued apologies to former Culture Secretary Tessa Jowell, her estranged husband lawyer David Mills and footballer turned broadcaster Andy Gray.
Mr Andrew, Ms Phillips and Joan Hammell, a former special adviser to Lord Prescott, are also believed to have received apologies through their solicitors.
News International said the move applied to allegations of voicemail hacking at the News of the World from 2004 to 2006.
Designer Kelly Hoppen is also understood to have been issued with an apology, although only for that time period, and not for a later claim.
No one else is understood to have received an apology. Other figures who have pursued the matter through the courts, including former Hull MP Lord Prescott, are not thought to be covered by the admissions.
The controversy has been a source of continuing embarrassment for News International.