In the face of hostility from Britain’s largest newspaper groups, David Cameron insisted today that cross-party plans for a press regulator would “work and endure”.

They have signalled their anger over the imposition of what they have described as “several deeply contentious” issues in a Royal Charter announced in Parliament by the Prime Minister.

After more than 100 hours of talks, David Cameron, Nick Clegg and Ed Miliband shook hands yesterday on an agreement which means that for the first time the British press regulation will be subject to an element of statute.

As the newspaper groups deliberated over their formal response, the Prime Minister said: “I'm confident we’ve set up a system that is practical, that is workable, it protects the freedom of the press, but it's a good, strong self-regulatory system for victims, and I'm convinced it will work and it will endure.”

Mr Cameron was speaking as he and the Deputy Prime Minister, Nick Clegg, toured a south London nursery to highlight moves to boost child care support.

The Liberal Democrat leader said: “I hope that when [newspapers] examine the fine print, they will see that the incentives are strong and that it's worthwhile, not least in order to restore public trust in the conduct of newspapers, for them to join in with the system, and I very much hope they will.”

Meanwhile the Hacked Off campaign group warned today that newspapers should stop lobbying ministers over the creation of a new press regulator. Hugh Tomlinson QC, a leading member of the group which campaigns for tighter press regulation, said the newspapers had had the chance to make their case to the Leveson inquiry and should now accept its findings.

Hacked Off director Brian Cathcart accused some newspapers of an "abuse" of their power in an attempt to protect their own position.

Under the plan announced yesterday, a press regulator would be established through the vehicle of a Royal Charter with the power to order errant newspapers to publish prominent apologies and to fine them up to £1m. The charter is backed by a clause of statute inserted into the Enterprise and Regulatory Reform Bill.

The deal was reached after Mr Cameron made several late concessions to Labour and the Liberal Democrats, who had made common cause in their response to last year’s Leveson report into media standards.

The biggest newspaper groups were left furious by the developments, having been shut out of the negotiations even though representatives of the press reform group Hacked Off participated in discussions. A newspaper industry source said: “The newspaper industry only saw this at 4.30pm. None of this has the agreement of the newspaper industry.”

Five major publishing organisations - the Daily Mail Group, News International, Telegraph Media Group, the Newspaper Society (which represents the regional press) and the Professional Publishers Association (which represents the magazine sector) - released a joint statement expressing their dissatisfaction with the developments.

“We have only late this afternoon seen the Royal Charter that the political parties have agreed between themselves and, more pertinently, the recognition criteria, early drafts of which contained several deeply contentious issues which have not yet been resolved with the industry,” it said. “In the light of this we are not able to give any response on behalf of the industry to this afternoon’s proposals until we have had time to study them.”

A senior source told The Independent: “What we are making clear is that we have not agreed to any of this.”

It is understood that the newspaper groups are concerned about the powers of the new regulator to order front-page apologies and the lack of opportunity for the press to challenge appointments to the board of the new watchdog. There are concerns about the regulator’s arbitration service for civil legal claims which will be free to complainants and offer the chance of financial recompense.

By contrast, Brian Cathcart, director of Hacked Off, said: “We are very pleased this draft of the Royal Charter has been accepted.” He said that the supporting clause was “clearly a statutory protection”.

Hacked Off said three of its members had attended the late-night discussions on the charter: Hugh Tomlinson QC, the former Liberal Democrat MP Evan Harris and Brian Cathcart, a professor of journalism at Kingston University.

It emerged last night that the new provisions would cover news-based websites – including the online editions of national newspapers and sites such as the Huffington Post – but not broadcasters’ websites. It will also exclude bloggers, tweeters and social networking sites such as Facebook and Twitter and small publishers of special interest and trade titles.

Three newspapers – the Financial Times, The Independent and The Guardian – had previously said they would be prepared to accept an element of statutory underpinning in establishing a new self-regulatory system along the lines set out by Lord Justice Leveson.

Last night Chris Blackhurst, editor of The Independent, said: “Given that some newspapers and their journalists behaved very badly over a number of years leading to the creation of a judicial inquiry by David Cameron, today’s outcome was always probable.

“Ideally we would not want any new regulatory system at all, but that was never going to happen. This isn’t perfect but neither is it terrible. I don’t see anything in it that will threaten the sort of journalism we produce at The Independent.”

The agreement was widely welcomed in the House of Commons yesterday – although several Conservatives made clear their dismay that Mr Cameron had come close to breaching the Tories’ promise not to allow any new press law.

Douglas Carswell, the Tory MP for Clacton, used his website to attack the proposals as a “disaster in the making” and said that Britain was setting a bad example to other countries around the world. “I grew up in a central African country run by various dictators who controlled the newspapers,” he wrote. “Perhaps that is why I find the idea of state regulation of the press in Britain so shocking.”

Angie Bray, Tory MP for Ealing Central and Acton and a former ministerial aide, said she feared Mr Cameron had “dipped his toe in the Rubicon”, while Sarah Wollaston, Tory MP for Totnes, said the Royal Charter proposal could be “something we may live to regret”.

Mr Cameron scrapped the cross-party talks on press regulation after appearing to lose patience with the slow progress in the negotiations. Aides said his move had forced the hands of Labour and the Liberal Democrats and insisted that yesterday’s deal would not have been struck without his initiative.

However, he ceded ground on several crucial areas. He agreed that the Royal Charter could be established with some legal underpinning designed to stop its terms being altered. The Prime Minister dropped his resistance to Labour-Liberal Democrat demands on the prominence of newspaper apologies and who will be able to sit on the regulatory body.

He told the Commons his plans did not “cross the Rubicon” to statutory control of the press. He said the Royal Charter legislation was designed to “protect the Royal Charter not to regulate it”.

Mr Miliband said: “Today’s agreement protects the victims and upholds a free press. It is true to the principles of Lord Justice Leveson’s report.”

Points of contention: winners and losers

The Use of Legislation

The Royal Charter was a Conservative idea which Labour and the Liberal Democrats initially viewed with scepticism. But, having opposed statutory underpinning, the Tories were persuaded to include a clause in the Enterprise and Regulatory Reform bill to ensure the charter’s future integrity. Narrow Tory win

Membership of the New Regulator

David Cameron’s earlier Royal Charter had restricted membership of the regulatory body to persons who met with the “unanimous” support of the appointments panel. Labour and the Lib Dems argued this would mean that effectively gave the press – which has one member on the panel - a veto on appointments. The word unanimous has been removed. Clear Liberal Democrat-Labour win

Apologies

The Tory wording that the regulator could “require” apologies contrasted with the Labour and Lib Dem stipulation that the watchdog could “direct” such corrections – onto the front page if need be. To the anger of the press the Tories conceded on this. Clear Liberal Democrat-Labour win

Arbitration Service

The service allows free access for complainants and does not rule out third party complaints except when brought on clearly frivolous or vexatious grounds. Hacked Off is pleased. The press is concerned. Liberal Democrat-Labour win

Exemplary Damages

This contentious issue is not included in the document and is still subject to further negotiation. No result

Editorial Code

To be written by a committee dominated by editors and journalists. This was a sensitive area for the press, which was worried about being told by outsiders how to do its job. The board will decide if the code has been breached. Labour and Lib Dems wanted the board to approve the code and have given some ground. Narrow Tory win