First Minister Rhun ap Iorwerth has demanded a “new deal” for Wales from the UK government that would put the country on an equal footing with Scotland.

In a letter he said powers over policing, justice, rail and the Crown Estate should be transferred to Cardiff.

Speaking at Plaid Cymru’s conference in Llandudno, the party’s leader said Prime Minister Andy Burnham has promised him he would not undermine Wales.

Ap Iorwerth is expected to meet the prime minister, along with the first ministers of Scotland and Northern Ireland, at the end of the month.

The UK government said it was “committed to building a stronger and fairer Wales in a stronger and fairer United Kingdom”.

Plaid Cymru is gathering in Llandudno’s Venue Cymru for the first time since it won a historic victory at the Senedd election in May.

The party had won power for the first time, ending Labour’s 27 year control of the Welsh government.

Ap Iorwerth said the result amounted to a “new dawn” for Wales, and “the beginning of our work to give flight to a nation whose wings have been clipped for far too long.”

But he warned that the upcoming Welsh government budget process would be “tough”, and said he would have to “find savings where we can”.

The Plaid leader said his meeting with Burnham at the Commonwealth Games “did leave me feeling positive – here we had an experienced devolutionist who wanted to bring power and people closer together.

“But as the weeks went on, it became increasingly clear that the prime minister’s wave of new powers risked crashing against Offa’s Dyke.”

He accused Burnham of having a “devolution programme for England”.

Speaking to party activists, ap Iorwerth said: “I’ve looked him in the eyes and said do not undermine Wales as a nation. Do not bypass our Senedd. And he looked me in the eyes and promised he would not. I will hold him to that.”

Scotland’s government and parliament has more control over the country’s own affairs than Wales, where policing and justice are controlled in Westminster, and not Cardiff, and where rail is largely devolved.

Ap Iorwerth said his proposed “new deal” would “redress the historic unfairness of our fiscal and constitutional settlement and put Wales on an equal footing with Scotland as a bare minimum”.

“It remains my hope that the prime minister will listen in a shared spirit, and that he’ll see that the respect agenda between the Welsh and UK governments must work both ways,” he said.

“If he fails, Wales will know again that our best interests will never be served by Westminster, and that it matters little whether who lives in Number 10 Downing Street is an Evertonian or an Old Etonian.”

Ap Iorwerth has sent a 2,000 word letter to Burnham spelling out his requests.

Plaid Cymru won the largest number of seats at May’s election, and since the defection of Sarah Cooper-Lessad it has 44 in the Welsh Parliament chamber.

It is five short of a majority, and needs the help of at least one other party group to pass its spending plans next year. It has been in talks with Labour, the Tories and Reform.

Ap Iorwerth acknowledged a “difficult economic and fiscal backdrop” and said it would be a “tight budget”.

“There will be difficult decisions. The budget arithmetic requires us to be disciplined and resourceful.”

He added there was a need for a “serious and collaborative approach with other parties”.

“We’ll have to drive efficiency, improve productivity and find savings where we can; through consolidating and streamlining services, avoiding duplication and focusing on outcomes.”

But he said that had to be “free of the damaging approach of the parties on the right”, accusing them of defining “savings” and waste by “ideology”.

He said the UK government’s forthcoming autumn budget was a chance to “reverse the planned-real terms cuts” to the Welsh government’s own spending.

Plaid has long-called for Wales to receive substantial extra funds for rail. Ap Iorwerth said that should come “now, not the 2030s”.

In another attack on rivals, he asked “others in sincerity to consider whose side they are on”.

“Whose side are they on when it comes to protecting Wales from the poison of the far-right,” he said.

The party leader paid tribute to fire services who fought the summer’s wildfires, and said he would “not allow my government to burden my children and your children with the destructive legacy of complacency on climate change”.

He said they had provided an “immediate cash injection to prioritise the longest NHS waits”, and had moved “quickly to begin the rollout of the most generous childcare offer anywhere in the UK”.

The party eventually plans to roll out childcare to children as young as nine months before the next election.

The first minister said his government was “determined” to tackle problems in the NHS, saying “too many aspects of the service are unfair on patients and on our brilliant staff” and are “unsustainable for the future”, although he acknowledged he could not change the NHS “overnight”.

He said he would not “shy away” from tackling child poverty “because of a difficult economic and fiscal backdrop”.

Labour’s Burnham has promised to end triple lock for pensions from 2030 to fund a new national care service. The idea appeared to win praise from Plaid ministers on Friday.

Social care is the responsibility of the Welsh government, and how it spends its money is up to its ministers. Both Plaid and Burnham would face elections before the policy would come in.

Plaid Cymru promised to “make progress” on delivering a national care service in its manifesto for the Senedd election.

Speaking to BBC Radio Wales Breakfast, the Plaid leader suggested that he may spend extra funds that come to the Welsh government, if any came as a result of more social care in England.

Ap Iorwerth said Burnham’s policy was a “good direction of travel”, but he added: “We don’t know what the consequentials will be.”

At a conference fringe, the deputy minister for social care, Delyth Jewell, said Burnham’s announcement was “very brave” and that a Plaid Cymru Welsh government would “have to work with the UK government on this”.

But she said the building blocks were already being put in place in Wales.

Burnham had previously said he would be “open” to the idea of giving the Welsh government control over policing.

He has also said: “I have to respect the governments in the nations of the UK, and I will, and give a fair hearing to anything that is put to me.”

A UK government spokesperson said: “This government is committed to building a stronger and fairer Wales in a stronger and fairer United Kingdom.

“That’s why our focus is now on working with the Welsh government to empower local leaders and communities to deliver good growth and jobs in every postcode.”