The statement by the prime minister, who has told the EU it must accept her Chequers plan or nothing, amounts to a further of the UK’s red lines in negotiations with the bloc.
The EU has repeatedly and unanimously rejected Chequers, a stance confirmed by the 27 other EU national leaders at a summit in Salzburg last week.
The prime minister was asked by reporters flying with her to the UN in New York whether no-deal would be better than a Canada-style deal.
She replied: “I've always said no deal is better than a bad deal, and I think a bad deal, for example, would be something that broke up the United Kingdom. What we've put on the table is a good deal.
“It's a deal which retains the union of the UK, our constitutional integrity, it's a deal which provides for no hard border between Northern Ireland and Ireland, protects jobs and enables us to have good trade relationship with Europe and the rest of the world.”
The EU has said Ms May’s red lines of leaving the single market and customs union, leaving the jurisdiction of the European Court of Justice, and ending free movement mean that a Canada-style free trade agreement is the only realistic option on the table.
I've always said no deal is better than a bad deal, and I think a bad deal, for example, would be something that broke up the United Kingdom
The prime minister’s claim that such a deal would “break up the UK” is based on the suggestion that a customs border between Northern Ireland and Great Britain would amount to a breach of sovereignty.
One of these would be likely under a Canada-style FTA because it would not preserve frictionless trade between the EU and UK and would require border checks. But both sides say they do not want a hard border with Ireland, so the EU has proposed keeping Northern Ireland inside the EU customs territory so that none is required.
The bloc says that if the UK wanted to keep frictionless trade it would have to soften its red lines and do a deal like Norway and stay in the single market, and potentially additionally stay in a customs union too.
The resistance to a customs border may partly be explained by the fact it is a red-line of the DUP, the right-wing Northern Ireland unionist party on which Theresa May relies for a majority in the House of Commons. She however said no British prime minister could accept such a proposal.
There has been some movement on how to solve the Northern Ireland border question – with the UK making clear it would accept regulatory checks between Great Britain and Northern Ireland. The EU has also tried to move checks away from ports and further-in land, or have them done in advance – with both sides expected to come up with concrete proposals after Tory party conference next week.
On the question of what trade agreement could be signed, however, both sides are further apart than ever – with Chequers now a crater, rejected by Remainers, Leaves, and the EU alike, and the prime minister doubling down on it even after its rejection by everyone else.