In an interview with BBC News, Brown called for an investigation into alleged links between News International newspapers and what he termed the "criminal underworld".
Brown believes journalists working for News International used "people that were known criminals - people that in some cases had criminal records" to obtain stories.
He said he did not know "the level of criminality involved until now", but said the country has a "duty to clean this up entirely", with the press facing some serious questions.
Yesterday, Rupert Murdoch's News International was accused of obtaining information about the former Labour leader and his family, including medical data about his son's cystic fibrosis, along with details from his lawyer and bank account.
Brown, who stepped down as Labour leader after losing the last general election, accused The Sunday Times of running a story "with the purpose of bringing me down as a government minister".
The claim relates to personal details allegedly obtained for a frontpage Sunday Times report claiming Brown had bought a flat owned by Robert Maxwell at a "knock-down price".
Brown told the BBC that the story had been "completely wrong" but News International had been "trying to prove a point" and bring him down when he served as chancellor.
It is thought that The Sunday Times obtained the information by employing a 'blagger', who contacted Brown's solicitor and tricked them into handing over the information.
The former prime minister also said he was "in tears" when he was told by News International that The Sun intended to publish details of his son Fraser's medical condition.
"Sarah [Brown] and I were incredibly upset about it, we were thinking about his long-term future, we were thinking about our family," he said.
Brown said that he always sought to protect his family "from the glare of publicity", and never publically discussed his son's medical condition.
"You don't know how [the story] appeared, I've not questioned how it appeared," he said.
"I've not made any allegations about how it appeared, I've not made any claims about how it appeared but the fact is it did appear and it did appear in The Sun newspaper."
In response to Brown's allegations about working with known criminals, News International said it had "no comment". However, the company reiterated its position that The Sun is adamant that the methods used to obtain the story were sound.
News International has been beset by a storm of controversy ever since it emerged murdered schoolgirl Milly Dowler's phone may have been hacked by a private investigator working for the News of the World.
The 168-year-old Sunday tabloid has since been shut down, but it seems clear that the allegations of hacking and criminal activity will continue to dog News International over the coming months.