Sinn Féin will demand a referendum on the future of Northern Ireland if there is no deal on Brexit, because a hard border would be erected the instant the UK crashes out of the EU under World Trade Organization rules, the party’s leader has said.

Mary Lou McDonald said a hard border would be so damaging to peace and prosperity on the island of Ireland that the Irish would not just sit back and allow it to happen.

Before a meeting with Theresa May, she said: “I very much hope that it doesn’t but if, by accident or design, there is a crash or a no-deal Brexit, Mrs May and whoever is in No 10 needs to understand that in those circumstances the constitutional question would have to be put to the people of Ireland.”

“You could not countenance such damage and disruption to our island and imagine that we will simply be philosophical about it and move on,” she said.

The principle of self-determination for the people of Northern Ireland is enshrined in the Good Friday peace agreement and allows for a border poll if there is evidence that a majority in Northern Ireland would support the reunification of the island.

The government has said it would not put in border controls in the event of no deal, but under the most-favoured nation rules of the World Trade Organization, the UK cannot operate one set of rules for trade with the republic of Ireland and another for other trading partners.

Sinn Féin has seven MPs at Westminster, representing all border constituencies, West Belfast and mid Ulster, although it does not sit in parliament because of its abstentionist policy. It is the second biggest party with 30% of the vote, just behind the DUP at 36%.

McDonald said she would tell May “not to hitch herself “to the Democratic Unionist party, which she said was prepared to forfeit Northern Ireland’s future in order to preserve the union.

“Their position is irresponsible. It’s damaging, it’s reckless, it’s not sustainable and frankly they won’t get away with it,” she said. “The idea that Mrs May or any element of British politics would attach themselves or co-opt themselves into this agenda to me is deeply shocking.

“I think it’s incredibly short-sighted. If the idea here is that it’s all just political expediency and the survival of a Tory government well shame on them. There are deep strategic long-term considerations here and one of them is peace and stability in Northern Ireland.”

McDonald is in London for a day of talks, which also include a meeting with the Labour leader, Jeremy Corbyn. The meeting comes at a crunch time for the prime minister as the DUP digs in its heels and threatens to vote against a Brexit deal that involves any extra checks between Britain and Ireland as a solution to the Irish border question.

It is understood that May has accepted there would be some checks in British ports and premises for goods, particularly food, going from Britain to the island of Ireland as a means of preserving the integrity of the single market.

McDonald will also press May again on the legitimacy of the DUP in the Brexit negotiations. “She knows as well as I do that the DUP do not represent the will of the people or the majority of the people in Northern Ireland,” she said, in reference to the fact that Northern Ireland had voted to remain in the EU.

She also attacked the DUP claim that the constitution of Northern Ireland is at stake, arguing that it was completely protected by the Good Friday agreement.

She also said it was wrong to paint Northern Ireland as a region or country similar to Wales or Scotland because of its history and the disputed border that led to the troubles. “Mrs May knows that the stakes are very high for Ireland. She knows, as we all know, that Northern Ireland is a place apart, it is different,” she said.