More than 80 politicians from all three main parties sign a letter warning the prime minister that accepting statutory regulation of newspapers would undermine free speech.
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The intervention highlights the deep divisions on the key issue, after a group of 42 Tory MPs urged tough new laws to keep newspapers in check.
Mr Cameron will receive his copy of Lord Justice Leveson's conclusions this lunchtime, a day ahead of the official publication.
The prime minister, Labour leader Ed Miliband and Liberal Democrat Deputy Prime Minister Nick Clegg have all indicated they will support the judge's recommendations as long as they are "proportionate".
But, with his own MPs and cabinet badly split, there is speculation that Mr Cameron could offer parliament a free vote.
No form of statutory regulation of the press would be possible without the imposition of state licensing - abolished in Britain in 1695.
Conservatives make up the overwhelming majority of the signatories, including "big beasts" Liam Fox and David Davis, as well as media select committee Chairman John Whittingdale and 1922 committee chairman Graham Brady.
Labour's Kate Hoey and Frank Field, and Lib Dem John Hemming also backed the letter.
"As parliamentarians, we believe in free speech and are opposed to the imposition of any form of statutory control even if it is dressed up as underpinning," they argued.
"No form of statutory regulation of the press would be possible without the imposition of state licensing - abolished in Britain in 1695.
"State licensing is inimical to any idea of press freedom and would radically alter the balance of our unwritten constitution."
The letter insisted almost all the problems raised before Lord Justice Leveson concerned illegal activity, suggesting a failure of law enforcement.
It cautioned that statutory regulation could be counterproductive, giving chaotic online forums such as Twitter further advantages over "properly moderated and edited print journalism".
However, the politicians stressed that the "status quo is not an option", and endorsed senior newspaper industry figures' proposals for a stronger regulator that could impose million-pound fines.
"We cannot countenance newspapers behaving as some have in the past. The solution is not new laws but a profound restructuring of the self-regulatory system," the letter added.
Fraser Nelson, the editor of the Spectator, has said that the magazine will not be bound by any statutory regulation brought in following the Leveson report. In a leading article for this week's edition he writes:
"If the press agrees a new form of self-regulation, perhaps contractually binding this time, we will happily take part. But we would not sign up to anything enforced by government. If such a group is constituted we will not attend its meetings, pay its fines nor heed its menaces. We would still obey the (other) laws of the land. But to join any scheme which subordinates press to parliament would be a betrayal of what this paper has stood for since its inception in 1828."