Theresa May’s attempts to end the Brexit impasse have been dismissed as the “same old rhetoric” by Northern Ireland political leaders following last-ditch talks to salvage her deal.

The prime minister held meetings at Stormont on Wednesday, where she sought to convince the five main parties of her commitment to avoiding a hard border in Ireland.

But she faced accusations she’d turned up “empty-handed with the same old rhetoric, with no plan, no credibility and frankly no honour” and her attempts to find an alternative to the unpopular backstop mechanism were described as “chasing unicorns”.

DUP leader Arlene Foster also ramped up the pressure on Ms May to strip the backstop from the deal, saying MPs had given the prime minister a mandate to “replace” the insurance policy.

It comes as European Council president Donald Tusk drew fury from Eurosceptics by saying there was a “special place in hell” for Brexiteers without a plan.

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On a two-day visit to Belfast, Ms May set herself at odds with Brexit hardliners by saying she was seeking “changes” to the controversial backstop, rather than its total removal from the withdrawal agreement.

The backstop would see the UK tied to a customs union – and Northern Ireland bound to some single market rules – if a trade deal cannot be agreed.

The DUP and Ulster Unionists are vociferously opposed to the mechanism but Sinn Fein, the SDLP and the Alliance Party argue it is the only way to maintain a frictionless border post-Brexit.

Ms Foster told reporters at Stormont there had been a “useful engagement” with the prime minister where the party reminded Ms May of their opposition to the Irish backstop, as the DUP believe it creates divergence between Northern Ireland and the rest of the UK.

She said: “We reiterated again the fact that the backstop was the problem in relation to the withdrawal agreement and the Brady amendment that was put down in the House of Commons last week gives her the mandate now to go to Brussels as she intends to on Thursday and we look forward to hearing the outcome of that.

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“As I’ve said, the Brady amendment is clear in relation to the withdrawal agreement that the backstop needs to be replaced. That is her mandate and that’s what I expect her to take to Brussels.”

Sinn Fein president Mary Lou McDonald warned the prime minister that she risked breaking up the UK if she engaged in brinkmanship with the EU.

She said: “We have told her that the British strategy of running down the clock and playing a game of chicken with Ireland and Irish interests is profoundly unacceptable and wrong.

“We have told her that the days of Britain dictating to Ireland or Irish people, that those days are over and will not return.”

She accused Ms May of acting in “absolute bad faith”, adding: “If British politicians cannot accept the specific needs of this country, of the Northern Irish, if British politics is incapable of acknowledging and upholding the Good Friday Agreement and the hardening of the border, then the only last option – the backstop of last resort – is a referendum on Irish unity.”

Naomi Long, leader of the Alliance Party of Northern Ireland, said the prime minister gave no detail about what the “alternative arrangements” could be to replace the backstop in their meeting.

She went on: “I am tired of people chasing unicorns. It has to stop, we don’t have time.

“We need practical solutions that are going to actually address the realities that we are facing.”

UUP leader Robin Swann said if Ms May cannot negotiate an extension and no deal is reached, then she must introduce direct rule for Northern Ireland.