The first ministers of Wales, Scotland and Northern Ireland have begun meeting in Cardiff to discuss “working more closely” including on constitutional issues.

It is the first face-to-face meeting among the nationalist leaders since Plaid Cymru’s Rhun ap Iorwerth was elected in May, with all three wanting their countries to leave the United Kingdom.

But there are differences in what they are calling for in the immediate term; with Scotland’s John Swinney and Northern Ireland’s Michelle O’Neill openly talking about wanting referendums, while in Wales ap Iorwerth has ruled out pushing for one now.

Sinn Féin president Mary Lou McDonald is also attending.

Ap Iorwerth will hold further talks with Swinney in the afternoon in their roles as government leaders, with both men expected to sign an agreement on “future collaboration in areas of shared interest”.

For the first time since devolution began, Wales, Scotland and Northern Ireland all have first ministers who want to leave the United Kingdom, with the three meeting on Monday as representatives of their parties.

A Plaid spokesperson said ahead of the meeting that the “changing political landscape across these islands” meant there was a strong case for “practical political co-operation” on areas like energy, the economy and working with Europe.

They said that also included “the wider political and constitutional questions facing our nations and on the right to self-determination”.

Ap Iorwerth said May’s Welsh election had been “a turning point for Wales”, and that there was “a growing recognition that the Westminster model is no longer working”.

SNP leader Swinney told Radio Wales Breakfast it was a “significant and pivotal moment for the United Kingdom”, and that things had “changed forever”.

“The people of Scotland, Wales and Ireland have a right to self-determination,” he said. “They are entitled to decide on their own future.”

“Fundamentally what our discussions today are about are about recognising the significance of the moment we are in.”

Sinn Fein vice president O’Neill said the best interests of people across the island of Ireland “have never been served by those in Westminster”.

“However, change is happening right across these islands and we must be ready for constitutional change when it comes,” she said.

“The election of three nationalist first ministers for the first time on these islands is a clear indication that people see that Westminster is not working for the people of the North, Scotland or Wales.”

Mary Lou McDonald, president of Sinn Féin, told BBC Wales the trajectory for Wales, Scotland and Ireland to self determination was different, and that we were living through “history-making times”.

“Obviously we have different national stories, but we have one very critical thing in common and that is our absolute insistence that it is for the people of Ireland to decide the future of Ireland, for the people of Scotland to decide the future of Scotland and for the people if Wales to decide the future of Wales,” she said.

The meetings come days after the matter of Scottish independence resurfaced in the Commons.

During Prime Minister’s Questions on Wednesday, Andy Burnham appeared to indicate a second referendum could be held in Scotland if there was clear public support for a vote.

He compared the situation to the conditions for a border poll in Northern Ireland, explaining the Good Friday Agreement made clear a poll would be “considered by the Northern Ireland secretary when there is a clear consensus in the country, when public opinion has changed to the point where the call has to be considered”.

“I would say that it is exactly the same situation in Scotland,” he added.

The apparent softening in tone was welcomed by Swinney before Burnham clarified that another Scottish referendum remained “off limits”.

A referendum on Scottish independence in September 2014 saw the country vote to remain part of the UK by a margin of 55% to 45%.

But the dynamics in Wales are different to those in Scotland.

Ap Iorwerth, who was appointed the first non-Labour first minister of Wales after May’s Senedd election, has ruled out pushing for a referendum on Welsh independence during his party’s first term in government, saying he wanted to lead a “national conversation” about the issue.

His government intends to set up a national commission to “lay the foundations” for future plans for Welsh independence.

In the meantime, Welsh ministers are seeking extra powers to be transferred to Wales, including over policing and youth justice.

Burnham has said he is “open” to the idea.

In Northern Ireland, the first and deputy first minister have identical powers and responsibilities and the Democratic Unionist Party’s (DUP) Emma Little-Pengelly is the deputy first minister.

Little-Pengelly criticised O’Neill for attending Monday’s talks.

The talks are likely to cover the way the devolved nations are funded by the UK government.

Welsh ministers have long called for the Barnett funding formula to be reformed, claiming it disadvantages Wales.

However, it is argued Scotland does well from the formula.

Before he became prime minister, Burnham made the case for change, but on his recent visit to Wales he played down the prospect of reform.

The devolved leaders will meet the prime minister next month.

The UK government said: “The prime minister is committed to delivering change across all four nations of the United Kingdom and believes strongly in the union.”

Welsh Conservatives leader Darren Millar said: “Instead of obsessing about independence, the first minister should be focused on dealing with the crisis engulfing the Welsh NHS and the declining standards in Welsh schools.”

Reform UK Wales said: “Plaid Cymru is showing its true colours by meeting with Sinn Féin and the Scottish separatists.”