Heather Mills, the Hove-based former model and ex-wife of Sir Paul McCartney, has accused the Daily Mirror of hacking her voicemails.
She made the claim on Newsnight on BBC2 on Wednesday night (3 August).
And today Sir Paul McCartney, who was dating Miss Mills at the time of the alleged phone hacking, said that he would contact the police on his return to Britain.
Sir Paul, who used to share his seafront home in Hove with Miss Mills, is currently in America on tour.
Miss Mills said that she had had a row with Sir Paul in early 2001 and that he later left a message on her phone.
She said that a senior Mirror journalist who worked for Piers Morgan, who was then the Mirror’s editor, rang her afterwards and “started quoting verbatim the messages from my machine”.
She said that she told the journalist: “You’ve obviously hacked my phone and if you do anything with this story … I’ll go to the police.”
The response, she said, was: “Ok, ok, yeah, we did hear it on your voice messages. I won’t run it.”
Heartbreaking
Some reports said that Mr Morgan had admitted listening to the message in question in an article for the Daily Mail in 2006.
He wrote: “At one stage I was played a tape of a message Paul had left for Heather on her mobile phone.
“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.”
Miss 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.”
Mr Morgan gives a slightly different account in his book The Insider which was published in 2005.
Furious
He wrote: “We’ve got a story that Paul McCartney had a blazing row with Heather Mills in a London restaurant … Heather was so furious with him that she stormed out of the place.
“We put the usual call in to Geoff Baker, his PR, and heard nothing back.
“But our information was good so I stuck the story on pages one and seven.”
Mr Morgan, who now has his own show on CNN, added that he then received a call from Sir Paul, who asked him to pull the story – and that he did so.
The Mirror and Mr Morgan have both denied that any phone hacking took place at the newspaper.
Mr Morgan, who comes from Newick in Sussex, was previously editor of the News of the World.
He has recently wrung an apology from Corby MP Louise Mensch, formerly the novelist Louise Bagshawe, after she accused him of phone hacking.
He said: “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.”
He said that during the couple’s divorce case it had emerged that Miss Mills had leaked information about Sir Paul and her relationship with him.
MPs on the Commons select committee that recently questioned Rupert and James Murdoch about phone hacking at the News of the World suggested that Mr Morgan had questions to answer.