The church hall in Cardiff’s Canton neighbourhood was packed with Green party supporters who had spent Saturday canvassing ahead of next week’s crucial Senedd elections. Green party members from Northern Ireland, Sweden and Denmark had all joined the local campaigners, adding to the sense of momentum for the Welsh Greens.

After waiting for more than an hour, the crowd cheered when Zack Polanski, leader of the Green party of England and Wales, appeared from behind the nave, hugging the Wales leader Anthony Slaughter as he did so.

The pair had settled their differences after Slaughter criticised Polanski for sharing a social media post criticising the police’s handling of the Golders Green attack earlier this week.

“This is something that I haven’t expressed out loud before, but I’m going to express it out loud to you guys: I’m really excited to see those results roll in,” Polanski told the crowd.

“In Gorton and Denton I looked out and thought, ‘This is a crowd that wins things’. And I am having that same feeling right now.”

Polls suggest Plaid Cymru’s Rhun ap Iorwerth is likely to become Wales’s next first minister, ending nearly 30 years of Welsh Labour dominance in devolved politics. While Reform could win the most seats, most of the other parties have ruled out going into coalition with Nigel Farage’s party.

Ap Iorwerth is hoping to win enough seats to establish an independent minority government, but the Welsh parliament is designed to accommodate coalitions and cross-party collaboration. Recent polls suggest Plaid Cymru will need to rely on other parties – and the most viable option is the Green party, which also backs Welsh independence.

Slaughter and Polanski have emphasised throughout the election campaign that the Greens could be “kingmakers” in the next Senedd. As a potential junior partner in a Plaid Cymru government, they have vowed to push the larger party to be bolder on energy, climate and housing policy, as well as rent controls and council tax.

Liz Hughes, a 53-year-old former Labour supporter, said the Green party represented “hope not hate”.

“I understand the frustration people feel at the cost of living and how hard everything is,” she said. “But Reform doesn’t have the answers.”

Saturday’s atmosphere was unthinkable a year ago. Last summer, Slaughter said he was confident the Greens would get at least one seat in 2026, their first ever in the Senedd. Since then, Green party membership in England and Wales has tripled to 222,000. In February, one Senedd poll forecast the party gaining 10 seats, pushing once-hegemonic Welsh Labour into fourth place.

Winning five seats would make the Greens a formal Senedd party group, unlocking hundreds of thousands of pounds in public money that could transform the party from a grassroots movement into a mainstay in Welsh politics.

While canvassing on a sunny Saturday in April in Grangetown, a working-class neighbourhood in west Cardiff, almost every resident told Slaughter they would vote for him. Several said they were disillusioned former Labour voters; one said they did not think Plaid Cymru’s platform was progressive enough.

“Dedicated members have put in a lot of work over the years on councils, campaigning, to get the party to where we are today,” Slaughter said. “It’s really weird being recognised though. I’m still not used to it.”

The Greens are likely to pick up seats in the two new superconstituencies that Cardiff straddles. The party is also competitive in Ceredigion Penfro and Brycheiniog Tawe Nedd.

Six members will be elected in each constituency under Wales’s new, more proportional voting system: by the time the sixth seat on the list is decided, a few dozen votes could make the difference, which means the fight for the last seats in many places could be a battle between the Greens and Reform.

At the church hall, Tessa Marshall, the second Green candidate on the list for Caerdydd Penarth after Slaughter, said: “Voting Green won’t let Reform in … We can stop [Reform] from being the largest party.”

The party’s relatively slim Senedd elections manifesto was described by the Institute for Fiscal Studies as an “opening gambit for potential negotiations with other parties”. On Saturday, Slaughter called it “an outline of our priorities and ambitions for Wales”.

Pledges to replace council tax and business rates with new taxes based on land value could chime with Plaid Cymru promises to improve business rates and make council tax “fairer”. The parties are also aligned on expanding universal childcare provision.

Energy and nature policy may be thornier ground. Welsh-speaking rural and farming communities make up much of Plaid Cymru’s base, and the Welsh nationalist party is supportive of some nuclear power, including Wylfa on Ynys Môn (Anglesey), which is set to host the UK’s first small modular reactor (SMR) nuclear power station.

The party was ready for the challenges and responsibilities of government, Slaughter said.

“Our candidates aren’t professional politicians, they represent a diverse range of communities, they have had real jobs and real experience of struggling to make ends meet to support their families,” he said.

“That makes them more than qualified and competent to helm the scale of the change that is coming after lots of tinkering around the edges from establishment factions.”