Burnham cited the 2016 EU referendum and the 2014 vote on Scottish independence.

“What we find is that the risks that come from those situations take a long time to heal and it sets you right back, and you can’t focus on what’s right in front of us here and now,” he added.

“The cost-of-living pressures that are hurting people in Northern Ireland, the need to get that budget set so that public services can function as they should.”

He continued: “A decade since the Brexit referendum I think we’ve had too much division, too much arguing, too much backward-looking.

“We need to fix the things right in the here and now.”

After the meetings with politicians, No 10 said the prime minister agreed with the first and deputy first minister that “their shared focus must be on working together to deliver stability, stronger public services and the breathing space people need as they face cost-of-living pressures”.

He also “set out his determination to find a solution to the Northern Ireland Executive budget”.

Democratic Unionist Party (DUP) leader Gavin Robinson welcomed the opportunity to engage with the prime minister.

He said Burnham’s remarks on a border poll were “particularly encouraging” and were “putting to bed the nonsense” discussed in recent months.

Sinn Féin leader Mary Lou McDonald said the Irish republican party’s delegation had a “very frank and very forthright” meeting with Burnham following his remarks in which he ruled out a referendum.

“We have put it to him very strongly that burying his head in the sand is not a plan, not a strategy, not wise and not acceptable to us,” she said.