The complaints filed with the High Court concern Mirror Group Newspapers, which also publishes the Sunday People and the Sunday Mirror, The Daily Telegraph reported Tuesday.
The complainants, including one by former soccer manager Sven-Goran Ericksson, cover the time when Piers Morgan, now with CNN, was editor at the Daily Mirror (1995-2004). Morgan has denied any role in phone hacking.
The three other claimants were reported to be Shobna Gulati, a "Coronation Street" actress; Abbie Gibson, a former nanny for soccer player David Beckham, and former soccer player Garry Flitcroft, the Telegraph said.
The four charged the publication with "breach of confidence and misuse of private information" involving the "interception and/or misuse of mobile phone voicemail messages and/or the interception of telephone accounts," the Financial Times reported.
Mirror Group Newspapers has maintained its staff operates within the law and the Press Complaints Commission code of conduct.
A spokesman for Trinity Mirror, its parent company, told the Telegraph, "We have no comment. We are unaware action has been taken at the High Court."
Mark Lewis, the lawyer representing the four complainants, said the case against the Daily Mirror had no paper trail.
"There might not be a documentary smoking gun, but we will show there is a smoking bullet, the consequence of the actions."
Last year, the Rupert Murdock tabloid News of the World went out of business because of a phone-hacking scandal that eventually ensnared the publication's editorial staff and expanded to accusations against police and public officials.
During one of the inquiries the phone-hacking scandal spawned, Sly Bailey, one-time chief executive officer at Trinity Mirror, testified he thought it was unhealthy for a company to internally investigate unsubstantiated allegations made against it, The Guardian reported.
"There was no evidence and we saw no reason to investigate," Bailey testified in January. "We have only seen unsubstantiated allegations and I have seen no evidence that phone hacking has ever taken place at Trinity Mirror."