A group of free speech campaigners are planning to set up a rival system of press regulation which they say will be fully compliant with the Leveson plan.
Last week most national newspaper publishers and a number of major regional and magazine groups signed contracts on joining the Independent Press Standards Organisation. This new system of self regulation has been criticised for lacking independence from the publishing industry.
The Impress Project has been set up to develop an alterative regulator to IPSO- saying they could provide a better way of fulfilling Lord Justice Leveson's blueprint for self-regulation within the industry, at the same time as protecting press freedom.
Ipso is set to be up and running by May 2014.
The Impress Project, which is supported by former Sunday Times editor Sir Harold Evans, wants to set up Impress: The Independent Monitor for the Press.
The prospectus for Impress sets out a similar system of regulation to that proposed under IPSO. The main difference may be the fact that it would be more independent of publishers.
The Financial Times, Independent and Guardian have all yet to sign up to IPSO having previously raised concerns about its independence.
Impress founder Jonathan Heawood, a former journalist and press freedom campaigner, said the group would listen to, and learn from, the public.
He said: "In poll after poll, the public has asked for robust regulation which is independent of both press and politicians. The newspaper owners' regulator is not independent, but until today it's been the only show in town.
"The Impress Project is an alternative process with the public interest at its heart."
Heawood said one of the key differences from Ipso would be that Impress would offer arbitration to members and non-members alike. It aims to start a pilot arbitration scheme in early 2014.
He said he wanted to "have a conversation" with those newspapers that had not signed up for Ipso to see if they could offer an alternative process.
But he added: "If the people involved with Ipso would like to find common ground, I would welcome that. I'm not looking for a fight. But there needs to be more choice, especially for smaller publishers and online publishers."
Membership of Impress would be voluntary and contractual, he said, with editors sitting on its code committee. The board would have a majority of independent members and senior industry figures would also be able to join.
Sir Harold said: "I support these proposals for a regulator that would be wholly independent of government or commercial interests, committed only to enhancing the standards of the British press. The dual purpose of discouraging abuses and resisting encroachments on an essential liberty is altogether necessary to restore public confidence. It is a necessary condition of the freedom of the press to act in the public interest."
The Impress Project has published its prospectus online. Its trustees are Lisa Appignanesi, who has led free speech campaigns, journalist Isabel Hilton and Professor Alastair Mullis, head of the law school at Leeds University.