David Davis and Jacob Rees-Mogg insisted they were not seeking to oust Theresa May as they demanded that the prime minister abandon her Chequers proposals and adopt their alternative plan to maintain “a free-flowing” border with Ireland.

The rebel Conservatives unveiled a position paper on the Irish border from the hard-Brexit European Research Group (ERG), but were forced to downplay the idea of a leadership challenge aired by some ERG members in a meeting on Tuesday night.

Rees-Mogg said the goal of the ERG was not to challenge May but to force her to ditch the Chequers plan. “I have long said and repeated that policy needs to be changed, but I’m supporting the person,” he said on Wednesday. May was a “fantastic and dutiful” prime minister and she “has my support”, he added.

Speaking immediately after, Davis, the former Brexit secretary, said: “I think we have a very good prime minister and like Jacob I disagree with her on one issue, this issue,” as the pair tried to switch the agenda away from leadership speculation towards their counter proposals to No 10’s Chequers plan.

Their comments came after a group of about 50 ERG members – not including Davis or Rees-Mogg – attended an evening meeting at which the idea of challenging May was openly discussed among the MPs hostile to her Chequers proposals.

Senior ERG members were frustrated that leaks from the previous night were overshadowing the Irish paper, a document arguing that existing technology and arrangements could be expanded to prevent the return of a physical border in Northern Ireland.

However, to achieve that, the ERG conceded that the UK would have to sign up to “equivalence of UK and EU regulations” for food products and standards. Under May’s Chequers plan the UK would sign up to “a common rulebook” for food and goods, which ERG supporters complain would leave Britain a “rule taker” from Brussels.

A dozen Tory backbenchers attended the launch of the paper at the Royal United Services Institute in Westminster, including two former Northern Ireland secretaries, Theresa Villiers and Owen Paterson, and the influential ERG organiser Steve Baker. But there was no sign of Boris Johnson, who had turned up to a similar event the day before.

Few believe that the ERG, which claims to have a maximum strength of 80 MPs, has the numbers to win a vote of no confidence in May’s leadership if one were called. To win, May would need to secure the backing of 158 MPs – half the Conservative parliamentary party – meaning the principal emphasis is on challenging Chequers, as exit negotiations with the European Union reach their critical phase.

Quick guide Will the Chequers agreement survive? Show Hide Who dislikes the Chequers agreement and why? Noisiest in their opposition are Tory Brexiters, not least David Davis and Boris Johnson, both of whom quit the cabinet in protest. They argue that the promise to maintain a common rulebook for goods and other continued alignment will mean a post-Brexit UK is tied to the EU without having a say on future rules, rather than being a free-trading independent nation. Labour has also disparaged the proposal, expressing deep scepticism about the so-called facilitated customs arrangement system. What about the EU? Brussels has sought to stay positive, but has deep concerns about elements of the plan viewed as overly pick-and-mix, and thus potentially incompatible with EU principles. Michel Barnier, the EU’s chief Brexit negotiator, says he opposes both the customs plan and the idea of alignment for goods. He also makes plain his contention that the Chequers plan contains no workable idea for the Ireland-Northern Ireland border. But at the same time the EU has been careful to not entirely dismiss the proposals, raising the possibility it could accept some adapted version. Who supports the agreement? Officially, May and her cabinet, though even here the backing can seem lukewarm at times. Asked about Chequers, the home secretary, Sajid Javid, said it was the government’s plan “right now”, indicating alternative ideas could be considered. Is it doomed? Even May’s allies concede it will be a hugely difficult task to get the plan through parliament. Damian Green, the PM’s close friend and former de fact deputy, described the process as “walking a narrow path with people chucking rocks at us from both sides”. On the remain side of the Conservatives, the former education secretary Justine Greening called the Chequers plan “more unpopular than the poll tax”, saying May should start again from scratch. If anything can save the plan – and it’s an outside shot – it will be a combination of the hugely tight timetable and the fact that, as yet, no one else has yet produced a plan with a better chance of being accepted by parliament. What happens next? On 20 September, an informal gathering in Salzburg, Austria, will provide a snapshot of current EU thinking. Then, 10 days later, the Conservative conference could show the Chequers plan is holed below the waterline. If it survives these tests, the proposals will then reach the crucial EU summit Brussels on 18 October, with something final needed, at the very latest, in the next two months. PETER WALKER

Downing Street said “it did not have a message” to MPs plotting to remove May, but added: “We have a commitment to no hard border in Northern Ireland and we don’t believe the answer is to move the border. People want to live their lives as they do now and that’s what the Chequers proposal does.”

Whitehall sources said the ERG paper was essentially the same as the “maximum facilitation” customs proposal pushed by Davis and other Brexiters in the cabinet that has previously been emphatically rejected by the EU.

The report accuses the EU of ignoring unionist opinion in Northern Ireland in negotiations over the Irish border in favour of advice from Dublin. The deputy leader of Northern Ireland’s Democratic Unionist party, Nigel Dodds, praised the ERG paper, tweeting:

Nigel Dodds (@NigelDoddsDUP) Dodds responds to ERG paper pic.twitter.com/RdMFM6klqx

However the Irish government’s Brexit committee chairman Neale Richmond dismissed the ERG papers as “dreamland stuff” which he said “goes beyond cherry-picking”.

“Much of the suggestions made in this paper, while couched in academic language, are simplistic and ignorant,” he said.

He added that the paper focusses solely on agriculture and food, and did not have an understanding of the complex cross border service provisions such as healthcare and education, as well as common rules in every other trading sector.

Richmond said proposals for exemptions for small business would be “music to the ears” of smugglers currently in operation with dissident paramilitary organisations.

Lisa Chambers, the opposition Brexit spokeswoman, also said there were no “concrete suggestions” for goods and services not related to agriculture and food. “I can’t see that is going to work and do not see the EU accepting this,” she said. “The problems that exist with Chequers still exist with the ERG proposal.”

Earlier the European commission president, Jean-Claude Juncker, said the EU would always show “loyalty and solidarity” with the Republic of Ireland on the issue of its border with Northern Ireland. Delivering his state of the union speech, Juncker said: “We will defend all the elements of the Good Friday agreement. It is Brexit that risks making the border more visible in Northern Ireland. It is not the European Union.”

The ERG paper says larger companies could use “trusted trader” schemes to clear their goods for export and import, and other declarations could be incorporated into the existing system used for VAT returns.

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“The EU will be able to maintain the integrity of its internal market without erecting a hard border along its border with Northern Ireland,” it says, adding: “The one element of ‘alignment’ necessary is the maintenance of the current common biosecurity zone covering the island of Ireland, and this is not contentious.

“The necessary procedures described can all be implemented within the existing legal and operational frameworks of the EU and the UK, based on the mutual trust on which regular trade depends.”

The group claimed its proposals could be delivered without the need for any new infrastructure at the border and without weakening north-south cooperationor jeopardising peace.

However, the Northern Ireland Retail Consortium said the proposals on animal and plant checks were a “misapprehension” of WTO rules which contain no obligation to have mutual recognition on food hygiene standards. The EU has only agreed mutual recognition with EFTA and EEA countries such as Switzerland.

The consortium’s director, Aodhán Connolly, said the proposals to remain in the EU VAT system were not possible as that comes with European court of justice oversight. He pointed out that Norway doesn’t have full access to the EU VAT system “and it has a hard VAT border as well as border checks with the EU, something that both sides have agreed cannot be allowed to happen in Northern Ireland”.