Publishers including the Guardian, the Independent and the Financial Times have yet to sign up to IPSO, with Guardian editor Alan Rusbridger appearing to suggest uncertainty over the regulator's independence from the industry.
However, journalist and free speech campaigner Jonathan Heawood believes he has a viable alternative to IPSO with The IMPRESS Project.
"Regulation is a good thing for anyone who takes journalism seriously," Heawood told Journalism.co.uk, adding that he thought the Leveson Inquiry "came out with some quite sensible recommendations".
At the core of Leveson's final report, published in November 2012, was a proposal for independent self-regulation, or as Leveson put it, "independent regulation of the press organised by the press".
However, Heawood believes IPSO does not follow this model because it constitutes "pure self-regulation" as opposed to "independent self-regulation".
"The whole thing is still actively owned and controlled by the biggest publishers in the industry," he said.
By contrast, The IMPRESS Project will be regulated by a board elected by an independent panel, he explained.
A key aim of the project is to level the playing field between large, well-established news outlets and smaller publishers such as regionals and hyperlocals.
One way The IMPRESS Project aims to do this is by being "very committed" to arbitration, or resolving disputes outside the courts.
"If you're a small publisher and you receive a libel threat, I know from experience that most people are terrified because they may not have the funds to fight it," said Heawood.
"So most people tend to settle outside of court or take down whatever the piece was that was causing the problem."
By offering an arbitration service open to all, Heawood hopes to give smaller publishers the confidence to pursue stories without fear of "people with very deep pockets shutting down negative reporting".
The project also aims to raise press standards by allowing its members to display a kitemark on their website or publication as a sign of quality, something which was put forward as part of the Media Standards Authority proposal to Leveson during his inquiry.
Other elements of The IMPRESS Project include a "whisteblowing hotline" and a public forum to act as "a space for listening and learning", where people can post their views on journalism and press regulation.
"Phase One" of the project, which was funded by the Joseph Rowntree Reform Trust, has been to gather views from publishers across the UK, with Heawood meeting with "very local" publishers to get ideas and feedback on the kind of press regulation they would to see, although he is unwilling to name names at present.
Asked how he would get bigger publications such as the Guardian, the Independent and Financial Times on board with the project, Heawood said: "We're talking to them and we're keeping them posted with how it's going. And the arbitration, I think, is interesting to them."
"Ultimately those publishers will have to make a choice [between IPSO and IMPRESS] and I think at this point the choice is a very close one."
Phase Two of the project is the Indiegogo crowdfunding campaign, which aims to raise £25,000, with the money going towards lawyers, drafting rules and appointing an independent panel to elect the regulatory board.
The latter, notes Heawood, is "quite a careful process we have to follow to make sure we can't influence that appointment".
"So we recruit an appointment panel and the appointment panel appoints the board, according to the principles set out in the Leveson report."
The IMPRESS Project has some high profile supporters, including Guardian journalist Polly Toynbee and Sir Harold Evans, former editor of the Sunday Times, who has joined as a patron.
Author J.K. Rowling, who spoke out strongly against press intrusion during the Leveson Inquiry, has also said she will match all donations up to a total of £25,000, doubling whatever the crowdfunding campaign manages to raise.
Nine days off deadline, the campaign has raised just over £9,000.
However, unlike fellow crowdfunding platform Kickstarter, the rules of Indiegogo mean The IMPRESS Project will receive all donations even if the campaign does not achieve its fundraising target.
And with IPSO scheduled for launch in May, Heawood is confident that The IMPRESS Project will go ahead later this year.
In particular, he believes this alternative idea of press regulation will be of interest to those "coming at journalism from new angles," such as smaller publishers and hyperlocals.
"It's a way of demonstrating that they do have standards and that they're not just another blog," he said, "that they are trying to do something for society, or to hold the powerful to account."