Tory Eurosceptics expressed frustration as the so-called Brexit war Cabinet failed again to come to an agreement on a decision about what to do as an alternative to staying in the customs union.
Eurosceptics fear continuous delays will result in the UK never leaving the customs union and playing right into the hands of the EU.
Downing Street promised that the Government will publish a paper in June that will explain the final decision on what the customs arrangements will be.
It is said this will be most detailed document on Brexit since the 2016 EU Referendum and is said it will be published before a key meeting of EU leaders next month.
Brexit Secretary David Davis said the document, known as the white paper, would have “detailed, ambitious and precise explanations of our positions…it should set out what will change and what will feel different outside the EU”.
The EU’s chief negotiator Michel Barnier mocked the Mrs May for failing to have her Cabinet come to an agreement.
Mr Barnier boasted to Europe ministers it was “unnecessary to fight” with Britain because none of the two options, the customs partnership plan or “Max Fac”, are “realistic, no matter which one they choose”.
The customs partnership plan is a system whereby Britain collects tariffs for Brussels and then companies have to claim back rebates to benefit from any lower rates or goods that end up in the UK.
The alternative option that is desired by Brexiteers is known as maximum facilitation, or “Max Fac”, and it would rely on using technology to ensure post-Brexit customs checks are at a minimum and frictionless.
Two Cabinet groups have been set up by the PM to settle the pros and cons of both options, but ultimately failed to make any progress.
Tory Brexiteers have expressed concern that if no agreement is reached by next month then the UK will end up staying in the customs union.
One Tory source told The Daily Telegraph: “There is frustration that the Prime Minister is not gripping this, that she is refusing to make a decision. Delay only benefits the EU because it increases the likelihood that we will end up staying in the customs union if we can’t find an alternative.”
Mr Davis said the white paper will be “an opportunity to set out clearly to both a domestic and an EU audience the reasoning behind our approach, including where we think it is clearly in the EU’s interests as well as our own”.
On Tuesday Mrs May’s problems on got worse as the Scottish Parliament stirred a constitutional crisis by withholding its consent for the EU Withdrawal Bill.
MPs voted overwhelmingly to reject the Bill, a move that has not happened in the devolved Parliament since it was created in 1999.
Scottish Tories accused First Minister Nicola Sturgeon triggering this political crisis to push for a second independence referendum.