An independent watchdog with legal teeth should be created to oversee the press similar to other industry regulators, according to a number of Westcountry MPs.
Gary Streeter (South West Devon), Oliver Colvile (Plymouth Sutton and Devonport), Sheryll Murray (South East Cornwall), Geoffrey Cox (Torridge and West Devon), Neil Parish (Tiverton and Honiton) and George Eustice (Camborne and Redruth) are among 40 Conservatives to sign an open letter calling for tougher reforms than those proposed by the industry.
They argue a new system of self-regulation "…would lack independence and risks being an unstable model destined to fail". But in doing so they are opposed by some of their own party colleagues who are against statutory regulation of the press.
Lord Black, chairman of the funding body for the Press Complaints Commission, told the Leveson Inquiry into media ethics he wanted a form of 'muscular' self-regulation. That would mean a new organisation with the power to launch investigations and levy fines of up to £1 million.
But this is rejected by signatories to the letter who are pressing for a 'credible' new regulator.
Mr Streeter said this would be along the lines of other industry watchdogs such as Ofgem for energy and Ofwat for water.
The Conservative MP said: "I think the national press have behaved irresponsibly for at least a decade if not more. It's now time for there to be an independent regulator to make sure they act more responsibly."
Lord Justice Leveson is expected to publish the findings of his inquiry in the next few weeks.
The investigation has heard evidence on phone hacking from celebrities and victims of crime as well as embarrassing revelations about the close relationship between some politicians and the media.
MPs and peers who signed the letter said the Leveson Inquiry represented a "once-in-a-generation opportunity to put things right" and urged the Government to "create a genuinely independent system".
The letter adds: "After eight months, 650 witnesses and 6,000 pages of evidence submitted to the Leveson inquiry, we can be clear about two things.
"Firstly, that a free press is essential for a free society. Secondly, that there are fundamental weaknesses in the current model of self-regulation which cannot be ignored.
"No-one wants our media controlled by the Government but, to be credible, any new regulator must be independent of the press as well as from politicians."