Lord Fowler, chairman of the House of Lords select committee on communications, today suggested the scandal had represented "a massive conspiracy against the public".
He asked for assurance from the government that once criminal proceedings are complete, then an independent inquiry will be set up to find out where responsibility lies.
A relaunched investigation by the Metropolitan police into allegations of phone hacking is currently ongoing. In April News International admitted liability in a number of cases brought against the News of the World for phone hacking between 2004 and 2006.
It has since made a "sincere apology" to actor Sienna Miller in court last week, after she agreed a £100,000 settlement in the case.
Responding to Lord Fowler's question today, Baroness Rawlings, government spokesman for Culture, Olympics, Media and Sport (Arts, Culture, and Media), said her answers would only cover press regulations and not criminal aspects.
However, she said she fully understood his request for a further inquiry and that the government would monitor the outcomes of the current inquiries and "consider whether any further action will be necessary".
"We are witnessing a revolution in the information and communications world as in technology in general, of such galloping speed that I can only agree that constant monitoring is essential in case further action is needed."
Lord Ryder of Wensum added "the very close links" between senior police officers and newspaper executives should also be investigated.
Lady Rawlings said it was a "very delicate point" but added it was it was hard to see as this stage whether another inquiry on this, on top of those already taking place, would be of any use. But she said the situation was being "constantly monitored".
Lord Sugar added it was "ludicrous to suggest the editor of a national newspaper is not aware of where the information came from".
"In the past a journalist was actually given a custodial sentence for phone tapping. But isn't it the case that the editor is responsible for what goes in the newspaper and therefore he also should be given a custodial sentence and indeed the proprietor and the board of directors?"
Baroness Rawlings said: "When it comes to editors, I am afraid I am unaware of what happened there."
Image by Mike Fleming on Flickr. Some rights reserved.