Influential Tory Eurosceptic Jacob Rees-Mogg has warned that Theresa May's "customs partnership" model would effectively mean the UK would remain in the European Union.
The Prime Minister has put forward a hybrid "customs partnership" model which would see Britain collect tariffs on behalf of the EU for goods destined for the block, with firms potentially claiming back a rebate if products remained in the UK on a lower-tariff regime.
Mrs May hopes that the model would allow trade to take place with as little friction as possible, and would also not mean a hard border between Northern Ireland and the Republic.
Yet according to Mr Rees-Mogg, this would not work as "to be effective it would have to keep us in the single market as well," he told ITV's Peston on Sunday.
He said it would be "odd" for the Prime Minister to back a policy that effectively breached her commitment on leaving both the customs union and single market, two policies she has previously set out.
"We are supporting the Prime Minister in what she set out in the manifesto - most importantly because that is our deal with the voters - but also in her Lancaster House, Florence and Mansion House speeches," the 48-year-old said.
"I think it would be odd if the Prime Minister were to write one thing for the Sun on Sunday and for another thing to be going on in Downing Street," he said.
"I trust the Prime Minister not to do things that are odd."
A decision on the Government's preferred customs option has been postponed after Theresa May's Brexit "war cabinet" failed to reach agreement last week.
Many leading Tory remainers back the Prime Minister's proposal and have urged her to abandon her Brexit strategy, instead commit to a Norway-style approach within the European Economic Area (EEA) and European Free Trade Association (Efta).
They also believe that a customs partnership would be more likely to gain cross-party support from MPs.
Just an hour before Mr Rees-Mogg contested Mrs May's customs-partnership proposal, the shadow chancellor said that disputes over the customs union would cause the Conservative Party to "fall apart".
Appearing on BBC One's Andrew Marr Show, John McDonnell said he believed that instead, many Tory MPs would back Labour's plan for a new customs union and "getting as close to the single market as we possibly can".
He continued: "What we have said very clearly - and I think actually quite a lot of the Conservatives are going to follow us in this - we remain within the customs union during the transition period, we want to negotiate a customs union, that will solve the Northern Ireland border problem, which I think is intractable."
Also appearing on Marr, Business Secretary Greg Clarke suggested extending a transition period on customs with the EU.
Mr Clark said it could be a case of implementing a new customs arrangement "as soon as you can do", as he highlighted the threat to potentially thousands of jobs of additional border checks.
The Tunbridge Wells MP said it would take some time for new customs arrangements to be put in place, saying it was "possible" it may take until 2023 to put new infrastructure in place.
He added: "So what I'm suggesting is as part of the work over the next few weeks, I think it would be a mistake to move from one situation to another to a third.
"If we can make progress as to what, which I think we can, as to what the right arrangement is for the long term, then it may be possible to bring that in over that period of time."
Asked if the transition could be extended until Britain was ready, he said: "It wouldn't be a question of extending the transition. It would be, as it were, implementing as soon as you can do... there will be different parts that can be done immediately. There will be things that will take more time."
He was backed by former home secretary Amber Rudd, who said Mr Clark was right to argue the case "for a Brexit that protects existing jobs and future investment".
Mr Clark cited the example of Toyota, saying it was making major decisions about future production and there were fears over how the firm's "just in time" manufacturing model would operate with customs checks.
The company employs 3,500 people in the UK, Mr Clark said, adding that such jobs could be lost if the UK's customs model was not right.
He went on to say the customs partnership model meant parts could be imported without any checks at the border or paperwork.
Mr Clark added: "But it's not perfect, because what it means is that if we have imports from other countries where we've abolished the tariff, there has to be an arrangement where you pay back."
Business groups the British Chambers of Commerce and the CBI welcomed Mr Clark's comments, saying it was important to maintain the status quo on frictionless trade until a new arrangement is in place.
Meanwhile, Mr Rees-Mogg, chairman of the European Research Group of Tory MPs, dismissed Mr Clark's warnings about the impact of rejecting the customs partnership.
He told Robert Peston: "This Project Fear has been so thoroughly discredited that you would have thought it would have come to an end by now.
"We trade successfully all over the world. The delays on goods coming into Southampton are tiny.
"We will have control of goods coming into this country - we will set our own laws, our own policies, our own regulations, and therefore we will determine how efficient the border is coming into us."
Speaking about the 3,500 potential job losses at Toyota that Mr Clark raised, Mr Rees-Mogg said that 80,000 job losses had been predicted if the UK voted to leave the EU, but such an issue had not arisen.
Meanwhile, DUP leader Arlene Foster, whose party props up Mrs May's government in Westminster, said that she did not "believe that we have to stay in the customs union to have free flow between ourselves and the Republic of Ireland.
"We believe that there are ways to deal with this, and indeed, back in August of last year, as you know, the Government put forward various proposals.
"We were disappointed there wasn't the engagement from the European Union at that time."
Ms Foster continued that not being in the customs union did not mean there would be a hard border between Northern Ireland and the Republic.