The BBC programme spoke to a journalist who worked on the newspaper in the past decade who claimed to have witnessed the interception of famous people's voicemails on a daily basis.
The source said: "One afternoon in the newsroom I saw Liz Hurley's phone being hacked and a reporter listen to her mobile phone messages and take a note of what was said.
"Designated reporters would be doing it pretty much every day. One reporter who was very good at it was called the 'master of the dark arts'. At one point in 2004, it seemed like it was the only way people were getting scoops.
"If they didn't just randomly hack people in the news, they would use it to stand up stories that people had denied."
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The source also claimed that the Sunday Mirror hired a voiceover artist to imitate celebrities to gain access to confidential information.
"I was told he had successfully managed to get health records too," the insider continued. "He was such a god of a voiceover artist that he could pretend to be famous people or failing that he'd pretend to be their lawyer or someone related to them.
"I was told that we had got [actress] Leslie Ash's medical records from the 'dark arts'."
Meanwhile, former Daily Mirror journalist James Hipwell, who served prison time for writing about companies he held shares in, has told an Australian newspaper he is willing to testify that Mirror journalists were told to intercept the voicemails of celebrities in the late '90s.
Trinity Mirror Group said in a statement: "Trinity Mirror's position is clear. Our journalists work within the criminal law and the Press Complaints Commission code of conduct."
More on the phone hacking allegations:
> Piers Morgan defends 'witch-hunt victim' Rupert Murdoch
> The Sun on Sunday 'already being pitched to advertisers'
> Nick Clegg urges Ofcom to scrutinise News Corp's Sky stake
> Full coverage of the phone hacking scandal