Ministers signed off the plans on Tuesday despite objections from Boris Johnson, the Foreign Secretary, and Michael Gove, the Environment Secretary.
Around 150 MPs attended the meeting where the plans for the border were outlined.
"There is a majority in Parliament, business and the trade union movement that supports Labour's call for a comprehensive customs union with the EU after Brexit". Officials have warned it may not be in place until 2023.
Iain Duncan Smith said Eurosceptic MPs could accept a delay of "a month or two" for practical reasons - but making provision for it now was akin to "planning for failure".
"We haven't talked about Brexit here for some weeks - deliberately, as we assume that tolerance for this is limited".
But the source, familiar with the discussions in London, said aligning Britain with European Union import tariffs for an extended period could be part of a backstop arrangement in the event of a delay in the implementation of any Brexit deal.
They favor a streamlined customs arrangement known as maximum facilitation or "max fac". However, Mr Davis was reassured after securing improvements, while other Eurosceptics eventually chose to "swallow" the proposed backstop. Without an agreement, there is no transitional deal and the United Kingdom hurtles over the cliff edge at the end of March next year - few would pretend that the United Kingdom is ready for such an eventuality. But all problems are not magicked away.
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When it comes to the UK's future trade relationship with the EU, Theresa May has already said that she hopes to secure a deal that's good for both sides. This, should it happen, would infuriate hard core Brexit supporting MPs in government and on the back benches with some claiming that it would undermine the entire raison d'etre for Brexit (who knew there was one?).
"But according to stories running in the British Press, PM Theresa May will set out to the European Union her clarification on Brexit this week before they meet in June to discuss how to proceed", says Robert Carnell, an economist with ING Bank N.V.
Following the meetings, the Prime Minister confirmed that the UK's alternative "backstop" proposal would be produced "in due course".
She explained that the border had 270 crossings, some of them unmarked roads and rural lanes and she feared that they would be attacked. No 10 sources said last night that there was no plan to stay "in" a customs union and that this week's Brexit war cabinet discussed only the Northern Ireland fallback plan, not post-Brexit customs arrangements.
The source said on condition of anonymity that the government was trying to find a way to make the backstop arrangement with the European Union more acceptable to Britain, rather than seeking an extension of a transition period.
Until recently, "backstop" was a reference to the UK's government commitment in December 2017 for a customs solution that would help to secure an open border in Ireland even if negotiations failed.