Theresa May continues to believe the EU’s proposal for avoiding a hard border in Ireland is unacceptable, senior UK officials have stressed, after a plan to consider an extension to the post-Brexit transition period raised fears she was about to sign up to a Northern Ireland-only backstop.

The prime minister told fellow leaders on Wednesday evening she was open to extending the transition period – one proposal mooted during intensive talks over the Irish backstop issue, which broke down without agreement last weekend.

The EU has proposed that Northern Ireland in effect stay in the customs union and single market after December 2020, at the end of the transition period, should there be no deal in place that would avoid a hard border on the island of Ireland.

Arriving in Brussels on Thursday morning, May said: “The original proposal from the EU was one we could not accept in the UK. It would have created a customs border down the Irish Sea.

“Earlier in the year we put forward a proposal as to how to deal with this issue; a further idea that has emerged - and it is an idea at this stage - is to create an option to extend the implementation period for a matter of months, and it would be for a matter of months.”

Senior UK officials later played down the idea the move should be regarded as a significant concession – and suggested even if the UK signed up to a clause allowing an extension, it would not intend to use it.

Quick Guide Why extend the Brexit transition period? Show Will the proposal solve anything? The mooted extension to the transition period is a new idea being put forward by the EU to help Theresa May square the circle created by the written agreement last December and the draft withdrawal agreement in March.

That committed the UK and the EU to ensuring there was no divergence between Northern Ireland and the Republic of Ireland.

But it also, after an intervention by the Democratic Unionist party, committed the UK (not the EU) not to have any trading differences between Northern Ireland and Great Britain.

The problem is that these are two irreconcilable agreements. They also impinge on the legally binding Good Friday agreement, which brought peace to Northern Ireland and in some senses pooled sovereignty of Northern Ireland giving people a birthright to be Irish or British or both.

If the UK leaves the EU along with the customs union and the single market then the border in Ireland becomes the only land border between the UK and the EU forcing customs, tax and regulatory controls. The backstop is one of three options agreed by the EU and the UK in December and would only come into play if option A (overall agreement) or option B (a tailor-made solution) cannot be agreed by the end of transition. The Irish have likened it to an insurance policy. The new EU idea is to extend the transition period to allow time to get to option A or B.

But an extension is problematic for Brexiters and leave voters, who want the UK to get out of the EU as soon as possible.

The Irish and the EU will also still need the backstop in the withdrawal agreement, which must be signed before the business of the trade deal can get under way. Otherwise it is a no-deal Brexit.

Extending the transition into 2021 would mean another year of paying into the EU budget. Britain would have to negotiate this but it has been estimated at anywhere between £10bn and £17bn. Staying in the EU for another year would also mean continued freedom of movement and being under the European court of justice, which Brexiters would oppose.

“The key point here is that there would be no intention of actually implementing any extension,” the senior official said.

Asked whether mooting an extension meant the UK was willing to sign up to a Northern Ireland-only backstop – on the basis that it was unlikely ever to be triggered – he said: “We have said repeatedly that the backstop put forward by the EU is unacceptable; that remains the case.”

Some of May’s Conservative colleagues have been infuriated, and others baffled, by the idea of a longer transition, which would mean the UK remained subject to EU laws and regulations, in which it would no longer have a say – and would continue paying into the EU budget.

Backbencher Anna Soubry said: “She’s reneging on everything and pickling everyone off.”

Former Tory minister Nick Boles described the attempt to extend the transition period as a “desperate last move”, and suggested May was losing the confidence of her party.

He told BBC Radio 4’s Today programme the EU was demanding “humiliating concessions”.

“It’s a classic of negotiations that she keeps on thinking that one more concession is going to somehow [succeed], with one bound and she’s free, and she’s not going to be free, she’s getting ever more trapped,” he said.

The backstop, an insurance policy to avoid the imposition of a hard border between Northern Ireland and the Irish Republic, is the key remaining sticking point in the fraught Brexit talks.

May’s cabinet colleagues have insisted she cannot sign up to anything that would leave only Northern Ireland subject to customs and single market rules; and are also adamant the backstop cannot be indefinite.

May’s DUP allies, upon whom she relies on to get legislation through the House of Commons, have also warned her against making significant new concessions, and even threatened to vote down the budget if she entertains the idea of a Northern Ireland-only solution.

David Davis and Boris Johnson sought to step up the pressure on May by signing a letter, alongside other former cabinet ministers, urging her to reject any backstop at all.

“Talk of either a UK or a Northern Irish backstop is inimical to our status as a sovereign nation state. Both are unnecessary: indeed they are a trap being set by the EU which it is vital we do not fall into,” they said.

They urged the prime minister not to “engage in a show of resistance and a choreographed argument followed by surrender and collapse into some version of the backstop and Chequers”.

Privately, UK officials suggest they are only entertaining the idea of an extension in order to help oil the wheels of the negotiations. They have been desperate to avoid a repeat of last month’s Salzburg summit, where EU leaders openly expressed their frustration at what they regarded as the UK’s intransigence.

May had been urged to arrive at Wednesday night’s dinner with “new facts” to offer EU leaders; but the extension of the transition appears to be the only new idea that emerged.

EU officials were surprised by the prime minister’s sunny outlook in her address to leaders on the state of the negotiations. After May’s 15-minute presentation on Wednesday, the 27 leaders instead spoke of the “grave” state of the negotiations, and agreed to up their readiness for a no-deal Brexit, sources said.

“There is a certain difference in the assessment of where we are now,” admitted one senior EU official. “Where May certainly has to a certain extent a positive assessment of where we are, focused on the considerable progress that has been made on a number of issues and emphasises that a deal is in reach; and where I think the collective feeling among the EU27, I would say, is somewhat more sceptical and notes the lack of progress or at least the lack of agreement at this stage.”

However, UK officials said despite EU leaders’ decision to pull plans for a November summit to seal the Brexit deal, they were still hopeful a deal could be done. “Our point of view is just getting this done, as soon as we can.”

EU leaders have not ruled out the idea of a November summit, if Michel Barnier says enough progress has been made; but for the moment the next European council in leaders’ diaries is in December – leaving the government little time to get parliament’s approval.

David Lidington, effectively May’s deputy, conceded on Thursday that extending the transition would be likely to carry a cost – though he denied it would amount to billions of pounds.

“That would be one of the things that would be teased out in the negotiations,” adding: “There may be other approaches we can take.”

Xavier Bettel, the prime minister of Luxembourg, said the cost to the UK taxpayer of extending the transition period would only be settled once it was clear how much longer the country would remain under EU laws.