Oliver Letwin, Cabinet Office minister, proposes a body overseeing self-regulation by the media. Photograph: Anthony Devlin/PA Archive/Press Association ImaThe leaders of the three main parties are edging closer to an agreement on regulation of the press, Labour claims. At a meeting on Wednesday ministers conceded there might need to be parliamentary underpinning to ensure the plan for a royal charter to oversee the press could not be amended.The Tories insisted that David Cameron’s position had not changed, and that he remain opposed to statute in press regulation. Further meetings are likely in the new year following the meeting, described by all sides as a constructive session.Labour said that Oliver Letwin, the Cabinet Office minister and Cameron’s chief adviser at the talks, had for the first time accepted that there would need to be a parliamentary process to ensure his royal charter plan was not subsequently overturned by the executive.Letwin proposes a verifying body be set up by royal charter and be responsible for ensuring that a voluntary form of self-regulation continues to be effective.The body might meet infrequently but would need its own budget and secretariat and expertise, paid for by industry through a contract. The culture select committee could also audit the verification body and its decisions might be open to judicial review.To prevent the charter being amended Clegg proposes that its terms would be unable to be altered save by parliament and with a super majority of two-thirds of MPs, a device already used to entrench a five-year fixed term parliament.The meeting’s participants also appear to have accepted that statute might be needed to give newspapers incentives to join the regulator – such as exemplary damages claims if a newspaper breaches the law and has refused to participate in the regulating body. If legislation were required a single clause could be inserted into the courts bill that would not specifically refer to the press.Government sources claim the ministry of justice has advised higher costs for newspapers which breach the law and refuse to co-operate with the regulator.It was stressed that no decisions had been taken, and that some of the party leaders, including Nick Clegg, would meet victims through the Hacked Off campaign to talk about the progress of the inter-party talks.Ed Miliband said on Wednesday that any deal would need to satisfy victims, and that they should not be excluded from the process. Labour wants its draft bill, setting up a verifying body overseen by the lord chief justice, brought forward. It fears that a royal charter system could be amended on the order of a minister and that the Queen would have option but to accept ministerial advice.Other draft bills have also been prepared, including two by the Department of Culture, Media and Sport, and one by Lord Lester, the Liberal Democrat peer.Letwin is concerned that any law on regulation of the press, even if it appeared innocuous and confined to the verification body, would be open to amendment by parliament.Labour counters that a royal charter could be open to amendment by the executive, bypassing parliament.Labour sources said they also remained concerned that the newspaper industry could be backsliding on some of its previous commitments concerning accepting a tougher form of self-regulation in line with the proposals of Lord Justice Leveson.They said they feared that the resignation of the Times editor James Harding had altered the balance of opinion among newspaper owners and editors.The newspaper industry is due to meet on Thursday to discuss the progress it has made about agreements over the form of self-regulation favoured by Lord Justice Leveson in his report on press standards, including on issues such as fines, third-party complaints, the appointment of the regulator’s chairman, and the prominence of press corrections.