Boris Johnson has submitted his proposals for a new EU withdrawal deal, with a warning to Brussels that if agreement cannot be reached in time for the Brexit date of 31 October it will represent "a failure of statecraft for which we would all be responsible".
In a four-page letter to European Commission president Jean-Claude Juncker, Mr Johnson described his plan as a "fair and reasonable compromise" containing a new protocol aiming to resolve the thorny issue of the border between Northern Ireland and the Republic.
He said he hoped it would provide the basis for "rapid negotiations towards a solution" so the UK can leave in an orderly way in 29 days' time on Halloween.
Mr Juncker's office said the Commission president welcomed "positive advances" on full regulatory alignment of Northern Ireland with the EU on all goods, and the offer of controls on trade between Northern Ireland and the British mainland.
But Juncker said there were still "some problematic points that will need further work in the coming days" relating to governance and customs rules.
The Commission will "examine the legal text objectively, and in light of our well-known criteria" and there will be talks between negotiating teams over the coming days, Mr Juncker told the PM.
The prime minister said his proposal would remove the so-called "backstop" arrangements for the Irish border - which he described as a "bridge to nowhere" - from the previous withdrawal agreement secured by his predecessor Theresa May last November.
"The government wants to get a deal, as I am sure we all do. If we cannot get one, it would represent a failure of statecraft for which we would all be responsible," he told Mr Juncker. "Our predecessors have tackled harder problems: we can surely solve this one."
And he wrote: "Both sides now need to consider whether there is sufficient willingness to compromise and move beyond existing positions to get us to an agreement in time. We are ready to do that, and this letter sets out what I regard as a reasonable compromise: the broad landing zone in which I believe a deal can begin to take shape."
The UK offer proposes an all-Ireland regulatory regime not only for agriculture and food products, but for all manufactured goods, effectively creating a border down the Irish Sea with traders having to notify the authorities about the nature of every shipment between the British mainland and the North.
The Northern Ireland executive and assembly would have a veto before the arrangement comes into force in 2021, and its consent would have to be renewed every four years.
The offer insists that Northern Ireland must remain wholly within the UK customs area after the end of a transition period in 2021, meaning customs checks will be required between the Republic and the North.
Both sides must agree that these checks will never take place at the border, but will instead be carried out electronically or in physical inspections in traders' premises or at other points on the supply chain. Some small traders will be exempted from the customs scheme.
Northern Ireland would be offered financial support under a New Deal to boost economic growth, improve competitiveness and fund infrastructure projects - some of them on a cross-border basis.
The plan won early backing from the Democratic Unionist Party, which said in a statement: "This offer provides a basis for the EU to continue in a serious and sustained engagement with the UK Government without risk to the internal market of the United Kingdom."
Mr Johnson said the plan was "entirely compatible with maintaining an open border in Northern Ireland" and would guarantee the UK control of its own trad policy.
And he said it would provide North-South regulatory alignment for a "potentially prolonged period" while resolving one of the key shortcomings of the backstop by giving that the people of Northern Ireland the unilateral right to pull out of the arrangement.
The plan would mean "changes" for people on both sides of the Irish border, but "our common task is to make sure that these changes entail as little day-to-day disruption as possible to the current situation", he told Mr Juncker, adding: "I believe that our proposals will achieve that."
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