A senior Mirror Group journalist admitted hacking voicemails left for Heather Mills by Paul McCartney, Ms Mills has claimed.
The journalist made the admission in 2001, Ms Mills told BBC2’s Newsnight programme.
McCartney's former wife said that after he left the voicemail, the journalist rang her quoting parts of the recording.
When challenged about how they knew what was said, Ms Mills said they admitted the message had been hacked.
The BBC, who declined to name the journalist allegedly involved, said it was not Piers Morgan, editor of the Daily Mirror at the time.
Mr Morgan issued a statement describing Ms Mills’ claims as “unsubstantiated”.
Ms Mills told the programme that in early 2001 she had a row with her then-boyfriend McCartney, who later left a conciliatory message on her voicemail while she was away in India.
According to Ms Mills, a senior Mirror Group Newspapers journalist rang her and “started quoting verbatim the messages from my machine”.
She 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 message in question appeared to be the same as one which Mr Morgan later admitted to listening to, a spokesman for the programme said.
In a 2006 article in the Daily Mail, Mr Morgan referred to hearing a recorded message which McCartney had left for Ms Mills, the spokesman said.
He wrote: “At one stage I was played a tape of a message Paul had left for Heather on her mobile phone”.
He added that it was “heartbreaking”.
“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, the spokesman said.
Ms Mills said: “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.”
In a statement issued through CNN, 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.
“The BBC has confirmed to me that this executive was not employed by the Daily Mirror.
“I have no knowledge of any conversation any executive from other newspapers at Trinity Mirror may or may not have had with Heather Mills.
“What I can say and have knowledge of is that Sir Paul McCartney asserted that Heather Mills illegally intercepted his telephones, and leaked confidential material to the media.
“This is well documented, and was stated in their divorce case. Further, in his judgment, The Honourable Mr Justice Bennett wrote of Heather Mills: ’I am driven to the conclusion that much of her evidence, both written and oral, was not just inconsistent and inaccurate but also less than candid. Overall, she was a less than impressive witness.’
“No doubt everyone will take this and other instances of somewhat extravagant claims by Ms Mills into account in assessing what credibility and platform her assertions are given.
“And 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 said it had learned that many other prominent people, including footballer Rio Ferdinand and TV presenter Ulrika Jonsson, also believe they were hacked by Mirror Group.
The spokesman said the programme understands Ferdinand believes an article in 2003 in the Sunday Mirror about his missed drugs test, which appears to have been 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 manager Sven-Goran Eriksson in 2002.
Mirror Group Newspapers is part of Trinity Mirror plc which publishes many titles including the Daily and Sunday Mirror, Daily Record and People.
A Trinity Mirror spokesman said tonight: “Our position is clear. All our journalists work within the criminal law and the PCC code of conduct.”
Last month a former Mirror reporter claimed that phone hacking was not confined to the News of the World but was widespread at other newspapers, including the Daily Mirror.
James Hipwell, who worked as a financial journalist under the editorship of Mr Morgan, said the practice was “seen as a bit of a wheeze” and offered to give evidence to the public inquiry into hacking ordered by Prime Minister David Cameron.
Hacking also took place at other titles in the newspaper group, including the People, he alleged.
Mr Hipwell was jailed for six months in February 2006 for pocketing nearly £41,000 by repeatedly purchasing low priced stocks, recommending them to readers in the Mirror’s City Slickers column and then quickly selling them as values soared.
Trinity Mirror said when Mr Hipwell made the claims that they were “totally unsubstantiated”.