When May outlined the idea at Mansion House in March, Johnson even posted a photo of himself holding a copy of the speech and giving a thumbs-up.
Mr Johnson said a customs partnership scheme would not see the United Kingdom "taking back control" of its trade policy, laws, borders or money after Brexit, raising suggestions he could resign from Government if his objections are ignored.
"It's totally untried and would make it very, very hard to do free trade deals", Johnson told the Daily Mail in an interview published late Monday.
Writing in the Daily Mail, he said: "If you have the new customs partnership, you have a insane system whereby you end up collecting the tariffs on behalf of the European Union at the United Kingdom frontier".
However, the spokesman insisted the Prime Minister maintains full confidence in Mr Johnson.
A decision on the Government's preferred customs option has been postponed after Mrs May's Brexit "war cabinet" failed to reach agreement.
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"I think it is a bit of an act of self-deception to say that we are leaving the customs union but we are still going to apply the common external tariff to all the imports coming in from the EU".
Shadow Brexit minister Baroness Hayter of Kentish Town said: "On the final day of Lords Report, the main focus of our cross-party efforts to ensure the Bill is fit for goal will be twofold. The prime minister asked officials to take forward that work as a priority".
Conservatives demanding a clean break have rejected two middle-of-the-road customs options May has proposed, with leading campaigners such as Foreign Secretary Boris Johnson fearing she will tie the United Kingdom too closely to the EU.
"The Prime Minister's plan would replace today's frictionless trade with a bureaucratic nightmare of tracking goods not just at the border but more or less anywhere and everywhere they are stored or distributed".
The company employs 3,500 people in the UK, Mr Clark said, adding that jobs had to be at the forefront of Britain's future customs model.
Her Remain colleague, Nicky Morgan, the former Education Secretary, also hit out at the "sabre-rattling and leadership threats" issued by Brexiteers and said the PM should not be "held hostage".
Ex-minister Ms Morgan added on BBC Radio 5 Reside that individuals who "shout loudest" do not symbolize most Tories.
His dismissal of the proposal stands in marked contrast to comments by Business Secretary Greg Clark on Sunday that the customs partnership option was still being considered by the government.