More than 50 victims of phone hacking, including a number of top celebrities, have written to David Cameron expressing fury at suggestions that the coalition government could reject tough new laws that would see the press policed by an independent regulator.

In a move designed to send the issue to the top of the agenda at the Tory conference, they warn the prime minister that trust in the media cannot be restored if the press is allowed to continue with a system of self-regulation.

Celebrities including Hugh Grant, Jude Law and Charlotte Church, as well as 7/7 victims and members of the Hillsborough Justice Campaign, have signed an open letter expressing alarm at reports that Cameron intends to reject any form of statutory regulation of the press if such a recommendation is made by the Leveson inquiry.

The judge-led inquiry into the role and governance of the media was established by the prime minister in July last year in response to the phone-hacking scandal at the now defunct News of the World newspaper. Having spent more than a year collecting evidence, the inquiry is considering a range of recommendations that may include a proposal for the press to be subject to an independent regulator backed by law and with significant new powers.

But the Hacked Off campaign, which represents victims of hacking and other forms of newspaper intrusion, and has issued the open letter, said it had become "alarmed and distressed" by reports that Cameron had decided to give news-papers "another chance to improve self-regulation".

Sources close to the prime minister have been quoted as saying he "is likely to reject statutory intervention in regulation of the press, even if it is recommended by Lord Justice Leveson".

When asked to comment last month, the prime minister's spokesman said only that the stories were "speculation". However, Hacked Off warns that any rejection of the inquiry's potential recommendations before they have been submitted to government would be "a betrayal of us and your previous commitments".

When he established the Leveson inquiry, Cameron pledged that the test for the future system of press regulation was not whether it suited politicians or the press but "people who have been caught up and absolutely thrown to the wolves by this process".

Hacked Off said it had also been concerned by comments made by Tory ministers. Appearing before the inquiry, the education secretary, Michael Gove, argued against the statutory regulation of the press and urged Leveson to "consider carefully" his proposals. Theresa May, home secretary, has given a warning on possible "unintended consequences" if self-regulation were scrapped.

Such a move would spark fury among some of the largest newspaper groups and prompt claims that the press was in danger of being muzzled. But a failure to be seen to act after a long-running and costly inquiry that he established would expose Cameron to claims that he was in thrall to powerful interests, notably Rupert Murdoch.

An alternative way forward, advanced by Lord Black, the chairman of the Press Standards Board of Finance, would be for a new self-regulatory press body that had the power to launch investigations and levy fines of up to £1m.

But Hacked Off said victims believed that any proposal that did not have a "statutory backstop" was inadequate. It said that it was seeking reassurances from the prime minister that he had an "open mind" on the matter and had "not already decided in favour of a proposal for continued self-regulation which we believe to be unsatisfactory".

The letter concludes: "We look forward to hearing from you as a matter of urgency so that our minds can be put at rest and so that the public in general may know that your position on this vital matter has not changed."

Professor Brian Cathcart, director of Hacked Off, said it was crucial that the inquiry's recommendations were not prejudged. "The victims of press abuse who signed this letter are alarmed that, before Lord Justice Leveson has even had the chance to report, it is reported that his proposals will be rejected," Cathcart said.

"It is hard to believe that the prime minister, who, after all, set up the inquiry, could really have taken such a decision. The judge has spent a year investigating press culture, ethics and practices; his recommendations, when published, surely deserve to be considered with open minds and with the greatest seriousness."

Dominic Crossley, who represented the families of Milly Dowler, and Madeleine McCann at the inquiry, said that it must be kept free from politics. "If Leveson's recommendations, whatever they may be, are ignored or diminished for purely political reasons, in face of what we heard of the relationship between the press and politicians, it would truly be scandalous," Crossley said. The Dowler family is not a signatory to the letter.

Church and Jacqui Hames, the former Metropolitan police officer who was targeted by private investigators working for the News of the World, will discuss their concerns with Cameron on Tuesday at the Tory party conference.

"We await Lord Leveson's independent report, the content of which is a matter for him," a Downing Street spokesman said.

• This article was amended on Sunday 7 October to clarify that the Dowler family was not a signatory to the letter to David Cameron