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.”
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.
Robinson said “clearly there are issues” around the budgetary settlement for Northern Ireland and it would form a key part of the DUP’s talks with the prime minister.
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.
