The “direction of travel” towards constitutional change is “clear”, the SDLP leader Claire Hanna has told her party conference.

“A new Ireland isn’t just on the table, it’s on the move,” she told delegates in Belfast on Saturday, in language which deliberately echoed the recent comment by the UK prime minister, Andy Burnham, that a Border poll on Irish unity was “off the table”.

Hanna said “more and more people are talking about our constitutional future” and it was “becoming clearer by the day that the future of this island is changing”.

“Don’t just take it from me, take it from the leader of the free world,” she said, in a reference to US president Donald Trump.

Hanna took to her feet in Belfast shortly after Trump, who arrived in Ireland on Saturday morning, told reporters he supported a united Ireland, saying “I’d love to see it unified” and it would be “a fantastic thing … a great thing”.

In her speech to the conference, Hanna acknowledged the US president’s presence on the island and reassured delegates: “Don’t worry, we’ve checked. He’s not coming here. It’s his turn to boycott us.

“Donald Trump, in the last hour, has announced that he is in favour of united Ireland. “Turns out he’s not as orange as he looks,” she said, in an allusion to the Orange Order.

“I’m not sure if anybody’s checked on the DUP,” she said. “I suspect they’re burning those Trump flags as we speak.”

But, she said, Trump’s comments underlined “as clearly as anything that change is happening, whether some parties here want to acknowledge it or not.”

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Emphasising how the SDLP was “shaping” the momentum towards unity, and in an implicit criticism of Sinn Féin, she said “we’re not just plucking dates for a Border poll out of the air, we’re doing the work, were building something different, something better and something new.”

“We’re talking about how it works, how we pay for it, how we protect rights and how we make sure that this change works for everybody, because the biggest question isn’t what date, the biggest question is why, it’s how … it’s who.

“Who do you trust to take you there?” she said. “Who do you trust to make Dublin and London understand that preparing can no longer be put off?”

The SDLP, she said, was “building a new Ireland, with a better Ireland along the way, and we need to be clear, those aren’t competing projects.

“They’re the same journey – reconciliation and constitutional change, improving life right now and setting up the future because we know you don’t get to a modern, plural new nation by running this place as a basket case.”

In a wide-ranging speech, Hanna also emphasised the achievements of the SDLP in Opposition at Stormont, including that “real institutional reform on Stormont is now very much on the table”.

“We turned years of ‘something must be done’ into a mandated plan for change,” she said. “We turned ‘that’ll never happen’ into Dublin and London now pressing the draggers so that an escape from the culture of vetoes and collapses is finally in sight.”

She was deeply critical of the Executive parties’ record in government, saying that the “early promise has already evaporated” and called on voters not to choose “another half decade lost to dysfunction and dither” when voting in the next Assembly election, expected in May.

“They’re all in government, they all have ministers, they all have power, and they have all had the chance and the responsibility to use it as the excuses pile up, the time slips away, and that’s another five years this region is never getting back.”