The Bishop of Norwich has called for a press regulator with guaranteed independence.
The Right Reverend Graham James wants a "fully independent body" with the powers to investigate press practices "without the trigger of a complaint bringing it into action".
The bishop was speaking in the House of Lords during a debate on the Leveson Report.
While the public response to the phone hacking scandal was "animated", he criticised a lack of repentance from newspaper editors for wrongdoing.
"Public moral indignation may still prove to be enough to reshape our culture, especially when it is in defence of the weak," he said.
Bishop James continued by saying that the lack of repentance cast doubt on whether self-regulation by the press was sufficient.
"Some elements of our national press have made the terrible suffering of such families almost unendurable," he said.
"In another age there might have been calls for public acts of penitence. The sad thing is that there has been surprisingly little public repentance and a great deal of self-justification and lapses of memory.
"This alone should make us wary of the claims of editors that they can clean up their act without the independence of their regulator being guaranteed by statute or in some other way."
He added: "Our newspapers have been very good at defending themselves from independent statutory regulation while calling for it in almost every other walk of life."
In sharp contrast, Bishop James noted that the Leveson report had praised local and regional papers.
"Regional and local newspapers are part of the communities they serve, strengthening our sense of belonging, providing information and exchange of ideas, celebrating what is good and reporting on what is disturbing," he concluded.
"Occasionally people say newspapers only report bad news. That's not true of our local and regional press."