Boris Johnson has struck a secret deal with the Democratic Unionist party involving radical proposals for a Belfast-Dublin “bilateral lock” on post-Brexit arrangements on the island of Ireland.

Details have emerged of the prime minister’s final Brexit offer that he will lay out on Wednesday, with Northern Ireland staying under EU single market regulations for agri-food and manufactured goods until at least 2025, at which point its assembly in Stormont will decide whether to continue alignment with EU or UK standards.

Johnson set up a high-stakes fortnight of talks with a threat that he will press ahead with a no-deal exit if the EU27 fails to engage with his plans.

No 10 is hoping the proposals will be enough to entice the EU back into negotiations ahead of the crunch EU summit on 17 October, with Johnson telling a reception at the Conservative party conference on Tuesday that the next 48 hours would be crucial.

The proposal that Ireland would have “two borders for four years” once the transition period ends after 2020 is likely to receive a frosty welcome in EU capitals. The broadcaster RTÉ quoted an Irish government source saying Johnson’s deal, as reported on Tuesday evening, would not be acceptable to Dublin.

However, DUP sources have confirmed that the party is largely “content” with the proposals, which are believed to still include a lot of elements of the backstop – a major concession for the party.

Q&A What is a Northern Ireland-only backstop? Show The British government’s version of Brexit involves the UK ultimately leaving the single market and customs union, requiring the return of a range of checks on goods crossing the border between Northern Ireland and the Republic of Ireland. The “backstop” is intended as a standstill placeholder to ensure such checks do not have to be imposed between Brexit happening with a deal, and the start of a new free trade agreement yet to be negotiated between the UK and the EU. Theresa May's withdrawal agreement proposed keeping the whole of the UK in a shared customs territory with the EU during this period. An alternative idea involves only Northern Ireland staying in the EU’s customs territory. That would place a customs border in the Irish Sea. May described it as a threat to the constitutional integrity of the UK, but the new prime minister, Boris Johnson, has opened the current talks by proposing an all-Ireland agri-food zone. The suggestion is that he will seek to quietly build on that with further NI-only arrangements. Given an NI-only backstop was an EU proposal in the first place, the U-turn would be warmly welcomed in Brussels, although attempts to give the Northern Ireland assembly a veto on its continuation would not be acceptable, and the DUP would be unlikely to support the prime minister in such a move in parliament. If there is a no-deal Brexit, then there is no backstop. Daniel Boffey

One central element of the proposals is expected to be a “Stormont lock,” giving local parties a say on any future proposals to keep the region aligned to EU rules and maintain an invisible border with the Republic of Ireland if Britain decided to diverge from European standards on goods and food.

Also crucial is the reestablishment of a newly empowered British-Irish ministerial council which was set up under the Belfast/Good Friday agreement but has not sat for three years. The restored council would give representatives from Stormont and the Irish parliament oversight on the future regulatory regime on the island of Ireland.

In his speech to the Conservative party conference in Manchester on Wednesday, the embattled prime minister will outline what he will call a “fair and reasonable compromise”, which Downing Street says has been drawn up after 70 hours of discussions with other EU member states.

He will insist that if the EU27 fails to engage with his proposals, he will press ahead with a no-deal Brexit at the end of October.

Brussels has warned there will be a cold reception if the offer resembles draft proposals leaked on Monday, which would involve customs clearance sites five to 10 miles from the Irish border – later denied by Johnson.

One EU source said: “Perhaps they realise if it’s anything that looks like what was floated in this leak, it is going to go down like a bucket of sick.”

No 10 briefed EU capitals on Tuesday on its controversial proposals and the plans are due to be published in full on Wednesday

Northern Ireland would not stay in the EU’s customs territory, as Johnson explained on Tuesday in a round of media interviews, meaning there would be two borders for four years.

Johnson told the BBC: “If the EU is going to insist on customs checks as we come out as it is, then we will have to accept that reality. And there will have to be a system, for customs checks away from the border. Now, we think those checks can be absolutely minimal and non-intrusive and won’t involve new infrastructure.”

The move by the UK to align with full EU regulations on goods for a period of four years has been privately welcomed by the EU member states.

The four-year time limit will dismay the Irish government, however. The taoiseach, Leo Varadkar, has repeatedly said such a time limit would be no better for Ireland than a no-deal today, given the uncertainty that would be created for the north-south economy.

The UK’s insistence that Northern Ireland will not stay in the EU’s customs territory, and that extra customs checks and controls would be required on the island of Ireland, is another major red line crossed for Dublin.

One source said the British-Irish council would be a “big part of moving along” the part of the backstop that was unattractive to the DUP – a regulatory barrier down the Irish Sea. It also would be a “double lock” on any move by Northern Ireland to diverge from EU rules applying in the republic.

“We need a mechanism so that the future relationship is not just left to London and Brussels,” said one insider. “A north-south ministerial council allows us to work things out between us.”

The proposals “deal with a lot of the issues the backstop was designed to deal with,” said a source close to the secret talks. “Everyone wants a deal. The DUP wants a deal, Dublin wants a deal, we want a deal. We are hopeful. It doesn’t mean we have the cake, but we are hoping we have the ingredients for one.”

However, the proposals risk a legal challenge as the Withdrawal Act 2019, also known as the Benn Act, bars any new infrastructure including customs checks on the border that did not exist before Brexit.

Johnson will tell the conference that even remainers now want to “move on” – a finding from recent focus groups. “Voters are desperate for us to focus on their other priorities,” he will say.

Cabinet ministers are bullish about the prospects of securing a deal before the 17 October European council – but sketchy about the details.

One told the Guardian they feared any bid to circumvent the Benn Act forbidding him leaving on Halloween without a deal would ultimately result in the supreme court forcing Johnson’s hand, but that by determinedly dubbing it the “surrender bill”, he had driven home the message that any delay would not be his fault.

However, Johnson will insist again on Wednesday that he will not budge from the Halloween deadline. “Let’s get Brexit done on 31 October so in 2020 our country can move on,” he will say.

The government has also opened up communications channels to Labour MPs in recent days in the hope that some who fear the consequences of a second referendum could yet support a Brexit agreement.

At a DUP reception, the party’s leader, Arlene Foster, put on a show of unity with Johnson whose speech was greeted with chants of “Boris, Boris” and “no surrender”.

She said the return of devolution to Northern Ireland was “critically important” and added: “I know a lot of people out there who want to get on with their lives, who are sick, sore and tired of listening to Brexit. They want to get Brexit done … we want to see an agreement reached.”

After his speech, Johnson said: “I’m not going to pretend this is going to be easy. This is not a walk in the park but we have made huge progress and I hope very much that in the course of the next two days we are going to get there.”

He said that after getting Brexit done, he wanted to put Jeremy Corbyn into a “figurative rocket” and “put him into orbit where he belongs”, with one audience member heckling with a violent suggestion that the Labour leader should face a “noose”.

As well as outlining his plans for a Brexit deal, Johnson will draw up battle lines for the general election – including seeking to bracket Labour with the Scottish National party, a move the Tories used successfully against Ed Miliband’s Labour party in 2015.

Johnson has also been keen to change the subject to domestic policy. There were some suggestions in Manchester that he could unveil a headline-grabbing tax cut on Wednesday to distract attention from the details of the backstop plan.