Britain's main political leaders are taking talks on the future of press regulation down to the wire amid signs that David Cameron is prepared to reach a last-minute deal to avoid a damaging defeat in the House of Commons on Monday.

As George Osborne insisted that the government was not "grandstanding" over the issue of press reform, the prime minister appeared to change tack by reopening talks with Nick Clegg, the deputy prime minister, days after abandoning all-party negotiations.

The renewed political discussions came as three of Britain's largest newspaper groups, including the owners of the Sun and the Daily Mail, ramped up the pressure by signalling that they were prepared to boycott the proposed press watchdog and set up their own body if Labour and the Lib Dems succeed in creating a statutory underpinning of the new royal charter.

The deputy prime minister found himself effectively acting as a go-between between the prime minster and Ed Miliband . Clegg spoke to the Labour leader on three occasions during the day – twice before meeting the prime minister and once afterwards.

The reopening of limited all-party talks came amid signs that Cameron is heading for a defeat in the Commons over tabled amendments to the crime and courts bill to establish exemplary damages for media organisations that do not sign up to a new regulatory body. Labour and the Lib Dems, who have 314 MPs to the Tories' 304 MPs, are planning to table their own amendments to strengthen the planned royal charter establishing the new body.

The Tories and Labour played hardball in what appeared to be something of an operation to paper over changes on all sides. Maria Miller, the culture secretary, was despatched on to the airwaves to say Labour had climbed down.

"Labour has been trying to push through a tough form of statutory regulation for the press with really unacceptable consequences for freedom of speech in this country," Miller told Sky News. "I think their climbdown from that position has put them much closer to our position and I think that is to be welcomed."

Labour dismissed Miller's remarks and insisted that it was standing by its core demands – statutory underpinning of the royal charter, a guarantee of prominent apologies by errant newspapers and no press veto on members of the new regulatory body.

A senior Labour source said: "We are in lock-step with the Lib Dems on this. We are clear we are not going to accept [Cameron's] royal charter. Any agreement must be on the basis of our royal charter. We are planning to go ahead with the votes in the Commons."

There was silence in Whitehall as the government parties prepared for another round of talks in the runup to the votes in the Commons.

The Tories claim that talks between the party leaders broke down last week when Labour sought to strengthen the royal charter on the basis of last-minute proposals by the Hacked Off campaign group. This prompted the prime minister to call for a Commons vote on his proposals.

One observer said: "It is like a game of poker. On Tuesday, the prime minister called their bluff. Then, at the weekend, when they published their royal charter and seemed to revert to their earlier position, they folded their hand."

This was dismissed by Labour which said the prime minister appeared to be changing his position. The chancellor indicated that Downing Street may be adopting a more flexible approach when he said he was still hopeful of an all-party agreement.

Osborne told the Andrew Marr Show on BBC1: "It would be great on Monday if we can get some kind of agreement, even at this late stage, between the parties. Frankly, press regulation that is achieved in a way that divides the political parties is not a press regulation that is really going to last and it is not a press regulation which is deeply rooted in our culture.

"I would say there is still an opportunity for us to get together and get a press regulation that works.

Ultimately we are not about grandstanding on this. We are about getting a press law that works and protects the press and gives justice to victims of press abuse."

It is understood that the prime minister may be able to live with a statutory underpinning of the royal charter – one of the key Lib Dem and Labour demands. The legal underpinning is designed to ensure that the royal charter can only be changed by agreement of two thirds of MPs, and not simply, like other royal charters, by ministers.

Cameron believes such underpinning is not necessary but is willing to be flexible because he has seen off what Osborne described as "some all-singing, all-dancing Leveson law".

But there are still differences over the composition of the regulatory body and on how apologies would be carried.

The prime minister is understood to share the concerns of many in the press that leading lights in the Hacked Off group, such as Brian Cathcart, could find themselves on the new body.

Downing Street said it was unable to answer the latest of several requests from the Guardian to reveal how many meetings the prime minister has had with editors, publishers or representatives of the press.