Heather Mills has alleged that a senior Mirror Group journalist admitted hacking voicemails left for her by her then-boyfriend Sir Paul McCartney.
Ms Mills told BBC Newsnight that after Sir Paul left the voicemail in 2001, the journalist rang her quoting parts of the recording.
When challenged about how they knew what had been said, Ms Mills said they admitted the message had been hacked.
Parent group Trinity Mirror says all its journalists work within the law.
Mirror Group Newspapers is part of Trinity Mirror plc, which publishes over 260 titles including the Daily and Sunday Mirror, Daily Record and People.
Trinity Mirror responded to the allegation by saying: "Our position is clear. All our journalists work within the criminal law and the PCC [Press Complaints Commission] code of conduct."
Ms Mills told Newsnight that in early 2001 she had had a row with former Beatle Sir Paul, who later left a conciliatory message on her voicemail while she was away in India.
According to Ms Mills, afterwards a senior Mirror Group Newspapers journalist rang her and "started quoting verbatim the messages from my machine".
Ms Mills said she challenged the journalist saying: "You've obviously hacked my phone and if you do anything with this story... I'll go to the police."
She said they responded: "OK, OK, yeah we did hear it on your voice messages, I won't run it."
The journalist whom Ms Mills said contacted her is not CNN presenter Piers Morgan, who was the editor of the Daily Mirror at the time.
However, the message in question appears to be the same as one which Mr Morgan later admitted to having listened to.
In a 2006 article in the Daily Mail, Mr Morgan referred to having heard a recorded message which Sir Paul had left for Ms Mills.
"At one stage I was played a tape of a message Paul had left for Heather on her mobile phone," he wrote.
"It was heartbreaking," Mr Morgan wrote. "The couple had clearly had a tiff, Heather had fled to India, and Paul was pleading with her to come back. He sounded lonely, miserable and desperate, and even sang 'We Can Work It Out' into the answer phone."
If Ms Mills' recollection is correct, the call Mr Morgan listened to had been hacked, and a fellow Mirror Group Newspapers journalist had tried to use it to get a story.
Ms Mills says: "There was absolutely no honest way that Piers Morgan could have obtained that tape that he has so proudly bragged about unless they had gone into my voice messages."
Mr Morgan, the Mirror's editor between 1995 and 2004, has consistently denied sanctioning any phone hacking.
In a statement issued through CNN on Wednesday, Mr Morgan said: "Heather Mills has made unsubstantiated claims about a conversation she may or may not have had with a senior executive from a Trinity Mirror newspaper in 2001.
"I have no knowledge of any conversation any executive from other newspapers at Trinity Mirror may or may not have had with Heather Mills.
"To reiterate, I have never hacked a phone, told anyone to hack a phone, nor to my knowledge published any story obtained from the hacking of a phone."
Newsnight has also learned that many other prominent people, including footballer Rio Ferdinand and TV presenter Ulrika Jonsson, also believe they were hacked by the Mirror group.
The programme understands that Manchester United and England defender Mr Ferdinand believes an article in 2003 in the Sunday Mirror about his missed drugs test, which appears to be based on text and voicemail details, involved the hacking of his messages.
And Ms Jonsson has also been told that she was hacked by the Daily Mirror as well as the News of the World in connection with her affair with then England football manager Sven Goran Eriksson in 2002.
Earlier, a former business journalist at the Daily Mirror alleged phone hacking was an accepted technique for getting stories, at the time Ms Mills says her phone was hacked.
The allegations made by James Hipwell, who has served time in prison for writing about companies whose shares he owned, were dismissed by a Trinity Mirror spokesman as "totally unsubstantiated".
So far, most of the revelations surrounding phone hacking have centred on the News of the World, which was published by News Group Newspapers until the paper's closure last month.
News Group is part of News International, a subsidiary of Rupert Murdoch's News Corporation.
Earlier this year, the NoW admitted intercepting voicemails, amid intense pressure from those who believed they had been victims.
Among them were celebrities, politicians and victims of crime.
In the following months, the NoW was shut down, a number of its former journalists and editors were arrested and News International executives were asked by MPs to explain themselves.
The prime minister also launched a judge-led inquiry into phone hacking and the ethics of the press.
Last week, amid the latest developments, Trinity Mirror announced it was to review its editorial "controls and procedures".
The company said this was being conducted in light of the current environment rather than because of a specific allegation.
Watch the full report on Newsnight on Wednesday 3 August 2011 at 22:30 BST on BBC Two, then afterwards on the BBC iPlayer and Newsnight website.