As well as customs, the white paper will cover the future security relationship, the financial services sector, aviation and fisheries. The EU has been calling for clarity, and sees the June summit as key milestone. As expected, there was no breakthrough.
Conservative MPs were invited into Downing Street on Monday for a briefing from the PM and chief of staff Gavin Barwell on the "customs partnership", believed to be Mrs May's preferred option, under which the United Kingdom would collect tariffs on the EU's behalf.
'Labour called for a white paper before Article 50 was triggered.More news: Lightning pull game back in Eastern Conference final
Two rival plans are being discussed and the one May backs-an unprecedented partnership that would keep close ties to the bloc-has been rejected by a majority of her inner Cabinet, including Brexit Secretary David Davis.
Davis reportedly told May that the customs partnership model she favours would be illegal under global law.
"In that scenario you'd end up staying in the customs union because you'd have no other choice", a senior source said.The attorney-general's office has been asked to provide an urgent legal opinion before the cabinet makes its final decision.
More than 90pc of the most important derivatives transactions in euros are cleared by British-based clearing houses, which, after Brexit, will be outside the EU. The advice will be provided directly to Mrs May and not considered by the cabinet sub-committee set up last week to examine the proposal's merits. Ministers have suggested that any decision could take weeks.More news: TI Arrested and Charged with Assault and Public Drunkenness
Mrs Hübner's European People's Party said in a statement that it did not want to force clearing houses to relocate but did want EU regulators to have more power over non- EU clearing houses if they dealt in euros. Though the bloc previously dismissed both options as unworkable, it has started to engage on May's partnership plan by asking for more details.
"What we need to do is, as she said, come out of the customs union in such a way as to enable us to have frictionless trade with no hard border in Northern Ireland".
"There is no doubt that a customs partnership hybrid model makes the Irish border situation easier, there is no doubt that the question of the Irish border is resolved by the customs partnership in an easier way than maximum facilitation". On May's preferred option, hurdles include the impact of Britain having its own independent trade and tariffs policy, and who would have jurisdiction over a dispute resolution mechanism.
"Instead, the prime minister has wasted months pursing her two fatally flawed customs options and presiding over a government that is too busy arguing with itself to negotiate for Britain".More news: Man Utd, Arsenal men among best stars to miss out
The government could be forced on Wednesday to publish the private papers that have been prepared for the inner Brexit cabinet to help break the deadlock in their negotiations.