The Brexit riddle of how to keep the Irish border free of customs checks - and even CCTV cameras and "smart technology" - when the invisible line becomes the only land border between the EU and UK remains unsolved and potentially catastrophic for the success EU-UK talks.
A No 10 spokesman said on Friday the United Kingdom did not recognise claims that its plans for the Irish border had been subjected to a "systematic and forensic annihilation" by European Union officials at a meeting this week with Britain's lead negotiator, Olly Robbins.
The UK hopes to avoid this outcome either by agreeing a very close economic partnership with the European Union, which it believes would make physical checks on the Irish border unnecessary, or the use of technology to keep goods flowing freely as they do now.
As recently as last week Boris Johnson said Britain couldn't stay in the customs union if it was to pursue trade deals.
The European Union has issued a fresh warning to the United Kingdom that a transitional deal after Brexit will not be secured unless the problem of the Irish border is resolved.
The vote, which has cross-party backing, would be non-binding but could be used by Tory whips to gauge the temperature of the Commons ahead of any similar vote which could force ministers to change policy on a future trading relationship with the EU.
"We are confident that in the coming months if all sides work together productively we can achieve a solution", British prime minister Theresa May's official spokesman said.More news: Beyonce Shuts Down Second Coachella Performance With Another Special Guest
More news: Quickfire Amir Khan wins comeback against Phil Lo Greco in 40 seconds
More news: Americans told to toss romaine lettuce grown over E. coli fears
The EU would not countenance allowing a country outside of its supervision and IT systems to levy duties, said it would place the burden of collecting tariffs on business and said that implementing the system on the EU side of the Channel would be too expensive.
"We want to use the positive momentum in these negotiations to finally settle outstanding issues, such as the solution to avoid a hard border between Ireland and Nothern Ireland", he said.
Lord Macpherson, the former top official at the Treasury, said the EU's position was "predictable" because of the backstop solution in the Withdrawal Agreement.
Mrs May will reportedly gather her "war cabinet" for weekly meetings as she tries to figure out a new solution to the border and customs union issues.
Chief negotiator Michel Barnier told French TV on Friday that 25% of the final withdrawal deal had still to be settled and it could still be derailed by disagreements over the border and other issues.
Open topics include the crucial issue of the Northern Irish border, and as long as these remain unresolved, "There are always difficulties, and risks of failure", Barnier said.
Labour MP Stella Creasy, said: "Just like David Copperfield in a Las Vegas courtroom this week, Theresa May's magical thinking, in her case about the Irish border, has been fully exposed".
The BBC understands that at a meeting on Wednesday with top United Kingdom officials, the EU's deputy Brexit negotiator, Sabine Weyand, went through the United Kingdom proposals "line by line" and explained why from the European Union side they had not changed sufficiently since previous negotiations and were still unacceptable.