The Brexit talks have reached a significant impasse over the issue of the Irish border, UK government sources have said, prompting Theresa May to update MPs in the House of Commons on the state of the negotiations.

No 10 indicated that a deal was being held up by renewed differences on the backstop arrangement insisted upon by the EU to prevent a hard border, after discussions came to a halt following a visit to Brussels by the Brexit secretary, Dominic Raab.

The prime minister’s official spokesman said: “The EU continues to insist on the possibility of a customs border down the Irish Sea. This is something which parliament already unanimously rejected and is not acceptable to the prime minister.”

The UK has proposed a “temporary customs arrangement” that would mean it adopting the EU’s common tariff policy from 2021 if no comprehensive free-trade deal can be signed before then to prevent the re-emergence of a hard border in Ireland.

But according to the UK, the European commission unexpectedly insisted on retaining the Northern Ireland-only backstop – as a “backstop to the backstop” – if the temporary customs arrangement was not ready in time. If imposed, this would place a customs border in the Irish Sea.

May will come to the Commons on Monday to outline the status of the increasingly fraught negotiations, amid intense pressure from hard Brexiters in the Conservative party to avoid a customs border in the Irish Sea and ensure any backstop is time-limited.

No 10 confirmed how to define the time-limited nature of the backstop also remained a sticking point. “We need to look the British people in the eye and say the backstop is a temporary solution,” May’s spokesman said. “We are not going to be stuck permanently in single customs territory, unable to do meaningful trade deals.

“The backstop needs to be a temporary arrangement, and there are a number of means of setting out what we want to achieve.”

Some cabinet members, such as the leader of the Commons, Andrea Leadsom, have privately indicated they want a specific date included in the backstop.

The prime minister will discuss the state of the Brexit negotiations in cabinet on Tuesday before heading to the European council in Brussels on Wednesday. EU leaders will discuss Brexit over dinner without May; it is not clear if she will have an opportunity to make a direct pitch to them before they talk.

However, the suggestion that the EU had surprised Downing Street by insisting the Northern Ireland-specific backstop would need to stay in the withdrawal agreement met with scorn from diplomats in Brussels.

EU negotiators had been open to introducing an EU-UK customs union, even on a temporary basis, which could supersede the backstop, in which Northern Ireland stays in the single market and the customs union as the rest of the country withdraws.

But diplomats noted the prime minister had repeatedly committed to a “specific” solution for Northern Ireland in the withdrawal agreement that would give the Irish Republic the necessary assurance that a hard border could never be introduced with Northern Ireland.

“If this is somehow a surprise, people have either not been focusing or they have been negotiating in bad faith,” one diplomat said. “The prime minister agreed this three times. Once in the joint report, again in March, and then in a specific letter to Donald Tusk [president of the European council].”

May had said in her letter to Tusk, which was demanded in March by the EU as part of an attempt to move the negotiations on, that she was committed to “specific measures in relation to Northern Ireland”, and would work on “a legal text for at least the ‘so-called backstop option’ set out” in last December’s joint report, which first introduced the need for Northern Ireland alone to stay in the EU’s structures.

Any sign of the prime minister giving way on the issue would prompt fury from her Democratic Unionist party allies. Sammy Wilson, the DUP’s Brexit spokesman, said it was almost inevitable the UK would end up with no deal.

“Given the way in which the EU has behaved and the corner they’ve put Theresa May into, there’s no deal which I can see at present which will command a majority in the House of Commons. So it is probably inevitable that we will end up with a no-deal scenario,” he told the Belfast Newsletter.

Raab had arrived in Brussels on Sunday unexpectedly, ahead of the crunch EU leaders’ summit at which the bloc has demanded “maximum progress” be made to allow the talks to develop.

He is understood to have told the EU’s chief negotiator, Michel Barnier, that the volatility of UK politics meant a plan to strike an agreement on Monday on the backstop was not possible.

Ambassadors for the EU27 were subsequently told on Sunday night by Sabine Weyand, the deputy chief negotiator, that the “Brits need more time”. “The problem is at the British end,” a diplomat said.

Speaking on Monday, the shadow Brexit secretary, Keir Starmer, rejected the idea of Labour helping May get a Brexit deal through parliament, saying his party would stick to its long-declared six tests for what constitutes a good Brexit.

Brexiter cabinet members have called a dinner meeting to be chaired by Leadsom to discuss their next move on Monday. Previous attendees of such meetings have included the international trade secretary, Liam Fox, the international development secretary, Penny Mordaunt, the work and pensions secretary, Esther McVey, and the transport secretary, Chris Grayling.

No 10 said it was relaxed about the meeting. “Cabinet members are free to eat whatever they choose,” the spokesman said. “Cabinet members have conversations all the time.”