Theresa May has said the UK will propose its own “backstop” solution for post-Brexit EU customs relations, to be put in place if no other deal can be reached.

Ms May informed top EU figures at a summit that the UK’s plan would be coming soon, with London having said the current backstop option is “unacceptable”.

It follows reports that the cabinet had agreed to keeping the UK in the EU’s customs union deeper into the 2020s, which Downing Street were quick to deny amid the threat of a Brexiteer backlash.

The current EU-proposed backstop is likely to see the UK staying aligned to the EU’s customs union until it has put in place the necessary infrastructure to implement a new customs policy, which officials have warned could be in 2023 at the earliest.

No 10 said that Ms May had discussed the UK bringing forward its own plan for a backstop with European Commission president Jean-Claude Juncker and European Council president Donald Tusk.

At a press conference in Sofia, she later said: “In December, [the UK and EU] set out clearly options in relation to the commitment that we have given for no hard border between Northern Ireland and Ireland.

“We expect that to be dealt with through the overall relationship we have with the European Union, but there were then two further levels of options including a final fallback option.

EU minister says little progress has been made on Brexit since March

“The commission published a fallback option which was not acceptable to us and we will be bringing forward our own proposal for that fallback option in due course.”

Cabinet ministers are currently unable to agree what kind of customs relations to seek with the EU after Brexit, and the EU has already rejected both of the options that they are arguing over anyway.

It means it is looking more likely that the UK will have to revert to the backstop option it agreed to in principle in December, that could see Northern Ireland remaining a part of Europe’s trading arrangements and a customs border drawn down the Irish Sea.

But with the government’s DUP political partners and the prime minister saying this would be untenable, it is possible that the whole of the UK would simply stay in alignment with EU arrangements – which in turn could anger Brexiteer backbenchers.

The cabinet is currently deadlocked over what kind of customs relations to opt for in the future – either a “customs partnership”, preferred by Ms May, or “maximum facilitation”.

The partnership plan would see Britain collect tariffs on the EU’s behalf at ports and airports, passing on a share of the money to Brussels – then, if the UK sets different tariffs from the EU, traders would claim refunds from HMRC for goods that stay in Britain.

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Olly Robbins, Ms May’s Europe adviser, regards the partnership as a means of avoiding a hard border in Ireland, while keeping the UK out of the European customs union. Close aides of Ms May have also called it “intellectually perfect”.

But Downing Street has been warned privately that the customs partnership proposal could collapse the government, with the Brexit-backing European Research Group having organised a critical report backed by 60 MPs.

The group’s chairman, Jacob Rees-Mogg, has called the proposal “cretinous” and “deeply unsatisfactory”, and argued that it would “not get us out of the European Union, which is what people voted for”.

The other option, also called “max fac”, is viewed more favourably by Brexiteers in both the cabinet and on the back benches, and would see the UK outside any customs union but with some controls at the border between Northern Ireland and the Irish Republic.

Backers say a “trusted trader” scheme and remote monitoring of the border would limit physical infrastructure.