At the time her phone was hacked in 2001, McCartney was Mills' boy-friend and the two married in 2002. They divorced in 2008.
The Mirror Group is part of Trinity Mirror, which publishes over 260 titles including the Daily and Sunday Mirror, Daily Record and People.
Mills told the BBC last night that a senior Mirror Group journalist admitted hacking voicemails left for her by McCartney.
She said that after McCartney left the voicemail in 2001, the journalist rang her quoting parts of the recording.
Mills said that in early 2001 she had a row with McCartney, who later left a conciliatory message on her voicemail while she was away in India.
Later, a senior Mirror Group journalist rang her and "started quoting verbatim the messages from my machine".
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 the person responded: "OK, OK, yeah we did hear it on your voice messages, I won't run it." 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."