The Independent is the only national newspaper title so far to indicate it will sign up to the new statute-backed press-regulator.
Parliament agreed legislation on Monday which ensured that the terms of the Royal Charter could not be changed without a two-thirds majority of both house and which put publishers outside the new state-recognised press regulator at risk of exemplary damages in libel trials.
The Independent argued in its editorial that it was time to "accept the new system and move on".
Financial Times editor Lionel Barber, which had previously indicated some support for a statute-backed solution, described the cross-party deal as a "horse traders' ball" and said that his newspaper had yet to decide whether it would sign up to the new arrangements.
"This has not been a satisfactory process. We have not decided at the Financial Times whether we are going to join up with the new regulator.
We will be looking at the practical implications and, above all, what has been completely lost in this process, the cost," he told the BBC Radio 4 programme The World At One yesterday.
"I am worried about the practical costs of, for example, allowing free access to arbitration, I am worried about claims-farming, vexatious complaints from readers and others who will tie us up in knots. This is a real problem."
There appears to be near universal condemnation of the way in which the final press regulation deal was hammered out – between representatives of Hacked Off and politicans in the early of Monday morning in Ed Miliband's office.
The Spectator has already indicated it will not sign up to the new system, with a front page this week which says simply "No". And Private Eye may continue its boycott of press regulation.
Spectator editor Fraser Nelson said: "Press regulation is too important an issue to be answered by some tawdry deal cooked up at two in the morning in Ed Miliband's office. It's not something the Spectator feels like signing up to."
Private Eye editor Ian Hislop said: "You cant really say this is a considered and thoughtful process when, in the middle of the night, bits are added to two different bills," he said. "This doesn't really look like thoughtful considered legislation that has been thought through."
Guardian editor Alan Rusbridger said he was broadly supportive of the new arrangements, although he expressed "grave reservations" over measures to enable the courts to impose exemplary damages on papers which did not sign up.
"The regulatory settlement is by and large a fair one, with compromises on all sides. We retain grave reservations about the proposed legislation on exemplary damages," he said.
"The agreed terms are not ideal, but after two years of inquiry and debate we finally have the prospect of a robust regulator that is independent of both press and politicians. It's a big improvement on what went before."
Associated Newspapers, Telegraph Media Group and News International have made clear they are strongly sceptical about the proposed press regulation deal. The Newspaper Society has said the libel arbitration system could prove "crippling expensive" for regional newspapers.
Publishers have already sought legal advice which suggests that imposing exemplary damages on non-members of the new regulator, and compelling newspapers to publish front-page apologies, could both compromise the Article 10 right to freedom of expression guaranteed under European law and in the UK Human Rights Act.
Lord Pannick, QC, one of the country’s top human rights lawyers, told The Times: "If the editor does not believe he or she should apologise, or does not agree with the content or the placing of the apology as required by the regulator, it raises real issues of freedom of expression under Article 10 for the newspaper then to be required to publish a specific statement in a specific place.”