More than 40 members of Britain's ruling Conservative party have urged Prime Minister David Cameron to impose tough new press rules overseen by regulators outside the industry, in an open letter published in the Guardian on Friday.

Senior members, including former foreign secretary Malcolm Rifkind and former party chairmen Caroline Spelman and Lord Fowler were among those calling for Cameron to reject the industry's recommendations for self-regulation.

"We are concerned that the current proposal put forward by the newspaper industry would lack independence and risks being an unstable model destined to fail, like previous initiatives over the past 60 years," said the letter.

Judge Brian Leveson is due to publish the findings of his inquiry into the culture, practices and ethics of the country's press before the end of the year, with many calling for statutory regulation to be recommended.

However, the letter warned against government interference in the running of the media.

"After eight months, 650 witnesses and 6,000 pages of evidence submitted to the Leveson inquiry, we can be clear about two things," it said.

"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," it added.

Brian Cathcart, director of campaign group Hacked Off, called the letter "a welcome development".

"We hope the Prime Minister will seize the opportunity presented by his own backbenchers and agree to hold cross-party talks on how to take forward Lord Justice Leveson's recommendations as soon as it is practical to do so," he said.