The judgement should be made by the “sovereign British government”, the international trade secretary said – two days after the cabinet was asked to back a joint review mechanism with the EU.
Significantly, Dr Fox missed that meeting, because he was on a trade trip to China, so missed the opportunity to give his views to the prime minister.
On his return, asked if a “mutually agreed withdrawal” was acceptable, he suggested it would fail to deliver the “instruction from our voters” given by the referendum.
“That decision can’t be subcontracted to somebody else – that needs to be an issue for a sovereign British government to be able to determine,” he insisted.
At stake is the fear of pro-Brexit Tories that the UK risks being locked indefinitely into the EU customs union – unable to sign its own trade deals – unless it can end the backstop unilaterally.
But Ms May has warned the cabinet that the demand must be dropped if the UK wants to secure an agreement with the EU within the next few weeks.
The backstop would keep the UK in the customs territory, after the transition period ends in December 2020, until an alternative solution is found to avoid Irish border checks – something dependent on unproven technology.
Dr Fox also insisted the cabinet must be given the “fullest possible information” before being asked to back the prime minister’s reworked plan, at a meeting now put back until next Tuesday.
Many other cabinet ministers are demanding to see full legal advice on the power to be conceded over ending the backstop, after Ms may indicated only a legal summary would be made available.
Meanwhile, in France, Jeremy Hunt played down the prospect of an imminent deal on Brexit, without which there is little chance of an emergency summit this month, to sign it off.
“Seven days is probably pushing it, but I am optimistic that there will be a Brexit deal but I wouldn’t want to be drawn on a specific timescale,” he told an audience at the British embassy in Paris.
EU chief Brexit negotiator Michel Barnier warned Wednesday that “more work is needed” in the talks, attempting to calm the speculation.
Mr Hunt faced suggestions that Britain is trying to withdraw from the EU, while retaining its trading advantages, but insisted the government was “not trying to have “our cake and eat it”.
Brexit will be discussed between Ms May and Emmanuel Macron, the French president, on Friday, when they meet in northern France for a ceremony to mark the end of World War I.
Dr Fox insisted he would not accept a Brexit unless “no part of the United Kingdom is treated differently” – and that the cabinet must see the full legal advice.
“It is really important that we feel we have the fullest possible information on which to make a decision that will have profound consequences for the future of our country,” he said.
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.