Peppiatt, who resigned from the title in March and passed his highly critical resignation letter to the Guardian, told the Leveson inquiry that he knew who had hacked his phone. The person was not on the payroll of Daily Star publisher Northern & Shell, he said, but seemed to be "in collusion" with the company.
He described an incident in which a message left for him by a friend had been deleted before he had listened to it and said he had received an email an hour later from someone else based on the information in the message.
"I never got the voicemail" Peppiatt said in court, having said in his written statement: "I see no way the information could have been known unless my voicemail had been accessed".
He told the court that he was unable to give any detail about the identity of the person he suspected was responsible as he was pursuing a civil case against them in court, but said that they were "long-established" and "linked to the tabloid world".
He also claimed that it was "very very likely" that they had received information from Northern & Shell, although maintained that he had not been directly employed by the company.
Peppiatt told the court that the alleged hacking was part of a campaign of threats and harassment against him after he leaked his resignation letter to the Guardian.
He received phone calls, he said, with threats including: "You're a marked man until the day you die"; "We're doing a kiss and tell on you"; and "RD's going to get you". RD, Peppiatt said, was likely a reference to Daily Star proprietor Richard Desmond, to whom the reporter had addressed his resignation letter.
Peppiatt said in his statement: "The police have now traced the source of this harassment and given him a warning. He is a person linked to the tabloid world but that I have never met, and who would therefore not have the indepth personal information he possesses without seeming collusion from the Daily Star/[Northern & Shell PR company] Outside Organisation.
"I am currently pursuing a civil claim against the individual to force him to reveal who ordered his behaviour toward me."
Peppiatt also described a "smear campaign" which he said was designed to discredit him, claiming that it was a common tactic directed at those who speak out about former employers in the tabloid press.
He said people like himself and former News of the World journalist Sean Hoare, who speak out about the culture in the industry, are "labelled as having axes to grind, somehow lunatics that aren't representing the industry fairly".
"That is the standard position that is taken," he added.
Northern & Shell issued a statement in the wake of Peppiatt's resignation, saying that he "worked purely as a casual reporter at the Daily Star" and "became unhappy after he was passed over for several staff positions".
The statement also claimed that Peppiatt had approached the newspaper with stories he said he was pressured to invent and vouched for their accuracy, and was "warned very recently by senior reporters on the paper after suggesting he would make up quote".
Peppiatt apologised during his testimony to the subjects of some of his stories for the Star, saying that he was "ashamed" and accepted that "no one forced a gun to my head".
"I do question my own moral judgement and behaviour and that I stayed as long as I did," he said.
Northern & Shell PR company Outside Organisation had not responded to a request for addition comment by the time of writing.
Also appearing at the inquiry today are Nick Davies, the Guardian reporter credited with many of the revelations that led to the phone hacking scandal, and Paul McMullan, former News of the World deputy features editor.