Theresa May is in danger of blowing open a major split at the top of the UK Government as she moves towards supporting a controversial customs partnership with the EU.

Underlining the tensions among her senior Cabinet ministers about which customs arrangement to adopt, Liam Fox, the International Trade Secretary, has insisted no form of customs union “could ever be acceptable” and hinted that if the UK were to move towards any such policy, he would resign.

Today, the Prime Minister will chair the 11-strong Cabinet sub-committee on Brexit – dubbed the War Cabinet – to decide which of two Government options on future customs arrangements Britain should adopt following the transition period from December 2020.

The Downing Street showdown will thrash out the pros and cons of each of two options – a new customs partnership and so-called maximum facilitation – in what is expected to be the most intense session to date of the sub-committee, with every member having his or her say. The sub-committee is said to be evenly split between the two options.

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It is thought Mrs May is keen to get the issue sorted out as the June European Council is fast approaching by which time officials from Britain and Brussels need to begin to finalise an agreement that can go before Europe’s parliaments and assemblies in October.

Appearing before the Lords EU Committee, David Davis told peers the Government would find it “difficult” to get any Brexit deal through Parliament unless it had achieved a “pretty substantive” agreement on future relations with the EU by the autumn.

The Brexit Secretary also warned the UK could be left “in a sort of limbo” if it was not able to complete a future relationship deal with the EU by the end of the transition period.

On future customs arrangements, the more pro-EU ministers support a “hybrid” form of the partnership option in which the UK would mirror the EU’s current custom arrangements for some sectors, effectively staying in the customs union for these, but for others would not, thus allowing it to cut trade deals with other countries in these sectors.

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Some in Whitehall have described this option as “intellectually perfect” but across the EU it might be regarded as Britain having its cake and eating it.

While this option would eliminate the need for a physical customs border, some ministers believe it is too closely retains ties with the EU, could threaten the UK’s ability to cut its own future trade deals and would be hard to implement because of technical complexities.

Leading Brexiteers Michael Gove, the Environment Secretary, and his Tory backbench colleague Jacob Rees-Mogg, have respectively described the customs partnership option as “bonkers” and “cretinous”.

They and other pro-Brexit Tory MPs back the highly streamlined “max-fac” option, which relies on new technology and “trusted trader” status to reduce trade friction. Yet this would keep some form of physical border between Britain and the EU.

Brussels has insisted both UK options are unworkable.

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The political stakes for the embattled PM are high given the Democratic Unionists, who are propping up her Government, have made clear they will withdraw their support if Northern Ireland is kept in any form of customs union.

At the weekend, friends of David Davis were calling for Olly Robbins, the chief UK official in the Brexit talks and said to be the main force promoting the hybrid customs partnership option, to be sacked. But the Brexit Secretary’s team later denied there was any move by Mr Davis to remove Mr Robbins from the negotiating team.

On Tuesday, Dr Fox argued that being in a future customs union with the EU would be “worse than the position in which we found ourselves today” as it would mean accepting EU-negotiated terms without Britain having had a say in them.

Asked if he would resign in such circumstances, the Scot replied: “We don’t answer questions with such suppositions” but then added: “Getting no answer, you can draw your own inferences.”