Theresa May will reject Michel Barnier’s revised Irish backstop border proposals at the Salzburg summit because the EU is still insisting on customs checks down the Irish Sea if the two sides cannot strike a free trade agreement after Brexit.

The prime minister foreshadowed the argument she will make to the other EU leaders over dinner on Wednesday evening in an article in Die Welt, which said the proposed backstop was “unacceptable” because it did not respect “the constitutional and economic integrity of the UK”.

May will arrive in Salzburg on Wednesday afternoon at an informal EU council during which will she will address Brexit over dinner and where EU leaders will discuss the issue again at lunch on Thursday in her absence.

The prime minister will also hold bilateral meetings on Thursday with the EU president, Donald Tusk, and Irish taoiseach, Leo Varadkar, as she seeks to end the impasse over the future of the UK’s only land border.

On Tuesday, Barnier said he was making revised proposals as part of an attempt to “de-dramatise” the issue, and tried to downplay them by describing them as “a set of technical checks and controls” and insisting that the EU respected the territorial integrity of the UK.

Barnier added that the bulk of the checks, for customs, VAT and excise and other regulations, could take place away from border points – although he conceded that increased sanitary checks for livestock might have to be done at the frontier.

May used her Die Welt article to push back at the critique made by Barnier and others of her post-Brexit vision, in her strongest terms yet. “There have been arguments made against our proposals that have been at odds with the reality of trade negotiations elsewhere and indeed the current trading relationship between EU member states,” May wrote.

Of the EU’s proposal that Northern Ireland in effect stays in the customs union and single market to avoid a hard border with the Irish Republic , she said: “Neither side can demand the unacceptable of the other, such as an external customs border between different parts of the United Kingdom – which no other country would accept if they were in the same situation – or the UK seeking the rights of EU membership without the obligations.”

The prime minister was due to make an appeal to EU leaders on Wednesday evening at the end of a dinner at Salzburg’s Felsenreitschule theatre, the scene of the Von Trapp’s family’s final concert in the film The Sound of Music. She is expected to tell them that Brussels needs to evolve its position as the UK has done, at the cost of two cabinet resignations.

The 27 EU leaders will receive a presentation from Barnier the following day, at a lunch where the heads of state and government will discuss the state of play of negotiations.

In the Chequers plan the UK has proposed a common set of rules on goods along with commitments in terms of subsidies, social and employment policies and environmental standards. It is also suggesting a customs arrangement that guarantees frictionless trade while allowing the UK to pursue an independent trade policy.

Barnier has claimed the proposals pose a threat to the European project, but May says the criticism is not grounded in reality.

She writes: “It is argued that one cannot separate goods and services. But no free trade agreement that the EU has ever concluded treats goods and services equally. And most relevant services for goods are not regulated by EU regulations anyway ... What we are proposing is a fair arrangement that will work for the EU’s economy as well as the UK’s, without undermining the single market.”

On Tuesday evening, Barnier said the EU was preparing to publish a new proposed solution to the Irish border issue, but he made clear that the fundamental principle of the region staying in the EU’s customs area was not being rethought.

Facebook Twitter Pinterest Michel Barnier, the EU’s chief Brexit negotiator. Photograph: Yves Herman/Reuters

In her article May reiterates her position that no British government could accept the EU’s proposed backstop, in which the region stays in the customs union and single market until a technological solution or a trade deal offers the same benefits.

The prime minister writes: “We will also honour our commitment to ensuring that there is a legally binding protocol on Northern Ireland, but this protocol must preserve the Good Friday agreement in its entirety and respect the constitutional and economic integrity of the United Kingdom, which the commission proposal does not.

“In order to achieve a good result, the EU now has to do so after the United Kingdom has developed its position … With goodwill and determination on both sides we can avoid a disorderly exit that would cause us all great difficulties and find new ways of working together.

“Whether we belong to the EU or not, we are part of the European family of states and must remain good friends who support each other in promoting prosperity and security.”