Lower fines for newspapers that sign up to an independent press watchdog would be enshrined in law for the first time under a "Leveson Bill" published by media reform campaigners.
Hacked Off has drafted a proposed law for England and Wales based closely on the recommendations made by Lord Justice Leveson after his inquiry into media ethics.
It claims the document, worked on by legal experts, undermines Conservative suggestions that legislation would be unworkable and offers a "plain and straightforward" way of implementing the findings of the 2,000-page report published last year.
The Bill, which has landed on the desks of Culture Secretary Maria Miller and Cabinet Office Minister Oliver Letwin, prevents political or government interference in newspaper content "unless it is for a legitimate purpose". The campaign group insists that would only apply to areas like Defence Advisory notices, formerly known as D-notices, which are issued to prevent publication of information for national security reasons.
The group insists the Bill would give the public access to a fair and free complaints system that would reduce the need for expensive court cases.
It would also protect newspapers from threats of legal action by wealthy individuals that are designed to frustrate and delay public interest investigations by the press, it adds.
A new watchdog would be obliged to ensure that the "privacy and dignity" of individuals are protected as well as creating a whistleblowing hotline for journalists under pressure to take action they feel is inappropriate.
Websites that write mainly for audiences in England and Wales but are based overseas would be eligible to sign up to the watchdog. The organisation hopes the Leveson-style "carrots and sticks" system, which would give publishers that agree to abide by the self regulatory body a cap on fines of 1% of turnover up to £1million, would encourage them to join.
Mrs Miller has made it clear she is reluctant to legislate for the system of statutory underpinning but ministers have floated the idea of establishing a Royal Charter to monitor the operation of the new press watchdog.
Hacked Off says fines not backed up in law would be difficult to enforce and is expected to hold further talks with the Culture Secretary about the reforms in the next fortnight.
Hacked Off director Brian Cathcart said: "Lord Justice Leveson conducted a thorough and painstaking inquiry, hearing all the evidence on all sides, and he delivered a thoughtful and balanced report, making clear recommendations on the best way forward.
"His report was very critical of the press and also of politicians, so neither group is in any position to quibble with his findings.
"The right thing to do now is to implement the judge's recommendations on press regulation in full and without delay. Our draft Bill - the Leveson Bill - offers a plain and straightforward way of doing that.
"This is not a Bill for press regulation as Hacked Off or anyone else would wish it: it is a Bill to underpin voluntary press self-regulation in the way Lord Justice Leveson wanted it.
"There are other schemes and ideas in the air, including other draft Bills and a proposal for a Royal Charter.
"None of these complies with the Leveson Report and all are likely to water down or distort his proposals. Only the Leveson Bill can deliver the considered and balanced new scheme designed by the judge to safeguard press freedom while at the same time protecting the public from press abuses.
"Hacked Off calls on all MPs, and peers and every group or individual interested in these matters, to read the Bill, participate in the consultation and give this process their backing, so that we can put behind us 70 years of editorial unaccountability and abuses. This is the best way to achieve a free and vigorous press that does not wilfully trample on the rights of citizens."