Senior EU officials have accused Theresa May’s government of putting its own survival ahead of the interests of the people of Northern Ireland, as they said they had lost all confidence in Downing Street’s capacity to navigate the Brexit negotiations successfully.

The prime minister was accused of a lack of “care” for the peace process by one senior EU official, who suggested that it was only the DUP’s hold over May’s government that was stopping Northern Ireland from effectively staying within the single market and customs union, and avoiding a hard border.

Arrangements for Northern Ireland similar to those adapted for Hong Kong and Macau, which are part of China but have their own trade regimes, would be acceptable to the EU. The province would stay under the body of EU law known as the acquis, allowing trade to flow freely on the island of Ireland, although it could lead to the erection of a border to trade between the province and the rest of the UK.

On Friday the Brexit secretary, David Davis, ruled out an arrangement that kept Northern Ireland under EU law, suggesting Britain would not accept anything that came with a “cost to the constitutional and economic integrity of the United Kingdom”.

A senior EU official with knowledge of behind-the-scenes discussions responded: “So far my impression is that this isn’t a priority for the UK. The UK doesn’t really care about the Irish. And maybe because of this lack of care, if it wasn’t for the DUP supporting the government, maybe this proposal of effectively staying in the EU could be the solution.”

The European parliament’s Brexit coordinator, Guy Verhofstadt, told the Observer that the British government, as a co-guarantor of the Good Friday Agreement, should be putting the interests of the people on the island of Ireland ahead of the survival of the Conservative party. He said: “Both the UK and the EU have a duty to work towards a solution for the people of the island of Ireland which avoids the reimposition of any kind of hardened border. It is crucial to safeguard peace and to preserve the Good Friday Agreement, which was brokered with the active participation of the European Union. … I hope the British government will do what is right for all the people of Northern Ireland. The peace process should transcend domestic party politics.”

I hope the British will do what is right for Northern Ireland. The peace process should transcend party politics Guy Verhofstadt

Beyond the issue of the Irish border, the instability of May’s administration, which has recently lost two cabinet ministers, is now affecting the negotiations, it is understood.

Paris and Berlin are pursuing an extremely cautious approach to preparing for talks on trade and a transition period due to the febrile nature of British domestic politics.

At a meeting of diplomats on Wednesday, it was agreed not to draft any substantive documents on the issues until Britain had moved forward on the key opening issues of the financial settlement, citizens’ rights and the Irish border. “We don’t want them to misunderstand us” and take progress for granted, said one diplomat. “We don’t want to go on the thin ice on this.”

A further concern is that the EU could push forward on internal preparations, followed by talks with the UK on trade and a transition period in December, only for May’s government to fall and for previous British pledges to be put in doubt.

A diplomatic source confirmed that the instability of the May government was the biggest risk to the Brexit talks. “If we get no deal, it is because of the complexities of UK politics.”

Even once the first phase of the negotiations has been successfully navigated, the EU fears the British government will not be in a position to agree on what it wants out of a future relationship with the bloc. “That’s why they are in cloud cuckoo land, or rather Boris Johnson land: have a cake and eat land. That’s simply because that is the only way to build a compromise in the cabinet,” the source said.

A second diplomat added: “We are not going around giving each other high fives every time there is a disaster. We are not even joking about it – because it affects us. A few weeks ago there was a lot of speculation about who would replace May, what it would mean, but now we are just numb to it, to be honest.”

Mujtaba Rahman, a former European Commission official, and now head of Europe for the Eurasia Group risk consultancy, claimed there was talk in Berlin of delaying the opening of talks on trade and transition beyond the European council summit on 14 and 15 December, even if ‘sufficient progress’ on the key opening issues was made by then.

It had been expected until now that the leaders would adopt the EU’s so-called guidelines, laying out its terms for a transition period and future relationship, at the same time as ruling that sufficient progress had been made for talks to widen.

“There is some pressure to decouple these things”, Rahman said. “The EU could afford themselves more time and adopt full guidelines [detailing their position] on trade and transition in January.”

“The EU has undertaken something of a crash course in British politics in the course of the last year,” he added. “The consequences of that is a reluctance to invest political capital in something that may not stand up.”

Andrew Duff, the former Liberal Democrat MEP, and visiting fellow at the European Policy Centre, which advocates a federal EU, said of his discussions with senior figures in the European commission and European council: “They are forming the impression that Britain is experiencing a kind of Weimar collapse. People are incredulous. It means a deal is increasingly improbable.”

A spokeswoman for the Brexit department said that it would “firmly reject” the suggestion that the government was putting its survival ahead of the interests of the people of Northern Ireland. “The government is committed to avoiding a hard border between Ireland and Northern Ireland,” she added. “As we said in our paper on the subject, the specific solutions to the unique circumstances in Northern Ireland must respect the integrity of the EU single market and customs union, and they must also respect the integrity of the United Kingdom.

“We respect the indivisibility of the four freedoms [the four pillars of EU integration, ranging from free movement of goods to free movement of workers] and that is why, as part of leaving the EU, we are leaving the single market and the customs union.”