A cross-party deal for a new press regulator underpinned by statute appeared closer today as Labour said it was "confident" reopened talks had secured the basis of an agreement.

The Prime Minister began last-ditch efforts to find an accord yesterday as he faced a likely Commons defeat on the issue later today with around 20 of his MPs set to back a rival package put together by an alliance of his Liberal Democrat coalition partners and the Opposition.

A senior Labour source said: "After five and a half hours of talks in Ed Miliband's office which ended at 2.30am, we are confident we have the basis of an agreement around our royal charter entrenched in statute."

The Conservatives were represented at the meeting by Cabinet Office Minister Oliver Letwin - who has been the key figure for the party in months of Leveson talks - and they were also attended by the Labour leader, Deputy Prime Minister Nick Clegg and shadow culture secretary Harriet Harman.

In Scotland, demands have been placed on the First Minister to debate the press recommendations for Scotland made by the McCluskey report in Parliament this week.

A Commons showdown was set up by Mr Cameron when he dramatically ended negotiations to find a way to implement the recommendations of the Leveson Inquiry into phone hacking.

He had said using legislation would "cross the Rubicon" and endanger press freedom, but appeared to soften his stance over the weekend

While Number 10 sources said the statutory underpinning was "unnecessary and undesirable", Mr Cameron signalled that it was not "a big issue of principle".

The Prime Minister, who met Mr Clegg to discuss the issue last night, is not thought to have yet signed off on any agreement, however.

Labour said it expected details to be announced in the Commons later today.

The Lib/Lab royal charter - a vehicle used to set up institutions such as the BBC, universities and professional bodies - is very similar in most respects to that put forward by the Conservatives.

It features tougher powers for the new watchdog to force newspapers to print prominent apologies and also rules out an effective industry veto over the membership of the regulatory body.

The main sticking point had been the insistence by Mr Miliband and Mr Clegg that legislation was required to underpin the system - attacked by critics as opening the door to future political interference.

Mr Cameron shut down the previous round of talks last Thursday, declaring that the differences between the two sides were too great and saying he would put the matter in the hands of MPs.

Tory sources blamed Labour for the collapse, claiming the Opposition put new demands on the table under pressure from the Hacked Off campaign group not to agree a deal - something denied by the Opposition.

But shortly after Mr Cameron published his royal charter-based regulation proposal - which he said would be the toughest ever that the British press had been subject to and include the power to levy million-pound fines - Mr Clegg broke coalition ranks to join forces with Mr Miliband.

They tabled amendments to the Crime and Courts Bill to entrench their alternative charter in law - setting up a Commons battle with the Tories.

Allies of the Prime Minister concede that in a hung parliament with no overall Conservative majority, he is likely be defeated in the division lobbies.

Tory former Cabinet minister Lord Fowler encouraged the party's MPs to rebel as the Lib/Lab plan "comes closest to implementing Lord Justice Leveson's careful and objective report".

News of the revived talks came after both Chancellor George Osborne and Culture Secretary Maria Miller indicated the door was open to a compromise.

"Ultimately we're not about grandstanding on this. We're about getting a press law that works," Mr Osborne told BBC1's Andrew Marr Show.

Mrs Miller said she hoped both sides could "come together and have a real solution here" but warned she still believed statutory underpinning would have a "chilling effect".

A Downing Street source said after the talks between Mr Cameron and Mr Clegg that they expected the negotiations to "go to the wire".

Mr Cameron insists he is acting as "a friend of the victims" of phone hacking, but one of them, author JK Rowling, said they had been "hung out to dry" by the Prime Minister.

Actor Hugh Grant, who fronts the Hacked Off campaign, said the Lib/Dem royal charter plan was not "ideal" but victims supported it and urged Tory MPs to defy Mr Cameron.

"MPs promised victims to do right by them and they have that chance on Monday," he said.

Tory Mayor of London Boris Johnson wrote that any form of statutory regulation of the press would be "potentially calamitous" for the UK's reputation.

"Anything remotely approaching legislation" will give politicians "the tools they need to begin the job of cowing and even silencing the press", he said.

At Holyrood, opposition parties have requested that Alex Salmond explains his "intentions" for the Scottish press after proposed regulations published last week were dubbed the "most draconian" of the western world by critics.

Lord McCluskey chaired a panel of legal experts and journalists who were appointed in December to consider the recommendations of the Leveson Report into press standards and how they may be accommodated in Scotland, under Scots Law.

Scottish Labour leader Johann Lamont wrote to Mr Salmond, after publication of the McCluskey report, to demand a full debate on the issue as soon as possible.

"This is too important to be left to briefings and the pages of the newspapers," wrote Ms Lamont.

"This week's business in Parliament is Government-controlled. I believe that we should have a statement and debate on the report's findings. Scottish Labour will, if necessary, provide space in our business time for whichever of your debates this week is moved."

The call was backed by the Scottish Conservatives, with leader Ruth Davidson saying: "Alex Salmond needs to clear up exactly what is going on here. His panel proposed some of the most draconian measures in the civilised world.

"Now that he's had time to digest this, he must explain as a matter of urgency what his intentions are for the Scottish press.

"If he continues to stall, the suspicion will be that he wants to hold the threat of state control over Scotland's newspapers on the run-up to the referendum."

Responding to Labour's demands, the Scottish Government said it was too early for such a debate.

A spokesman for the First Minister said: "The appropriate time to discuss these issues in Parliament is after the cross-party process has reached its conclusion. As the First Minister said on Friday we expect that to be after the Easter parliamentary recess.

"Meantime, the Scottish Government will take time to consider all of the suggestions in the McCluskey report and discuss their proposals with the representatives of all of the other political parties, including Johann Lamont, and with other stakeholders."