Two cabinet ministers have broken ranks to warn against moves by Theresa May towards a softer Brexit, with Liam Fox telling Conservative MPs that a customs union would be the “worst of both worlds” and Andrea Leadsom calling for changes to her deal with the EU.

Fox, the trade secretary, wrote to the Conservative backbench 1922 Committee to explain to MPs why he could not support a customs union with the EU, saying it would give other countries access to UK markets without automatically getting reciprocal access to theirs.

Q&A What is a customs union? Show Hide A customs union means that countries agree to apply no or very low tariffs to goods sold between them, and to collectively apply the same tariffs to imported goods from the rest of the world. International trade deals are then negotiated by the bloc as a whole. For the EU, this means deals are negotiated by by Brussels, although individual member state governments agree the mandate and approve the final deal. The EU has trade deals covering 69 countries, including Canada and South Korea, which the UK has been attempting to roll over into post-Brexit bilateral agreements. Proponents of an independent UK trade policy outside the EU customs union say Britain must forge its own deals if it is to take advantage of the world’s fastest-growing economies. However they have never explained why Germany manages to export more than three times the value in goods to China than Britain does, while also being in the EU customs union. Jennifer Rankin

His comments suggest he would be unable to remain in the cabinet if May were to agree to a customs union as part of talks with Labour, which are to resume on Tuesday at ministerial level.

Fox even suggests that he considers a negotiated customs union with the EU as a third party would be worse than remaining inside the customs union as a member state.

“We would be stuck in the worst of both worlds, not only unable to set our own international trade policy but subject, without representation, to the policy of an entity over which MPs would have no democratic control,” he said in a letter obtained by the Telegraph.

“This is something that Labour do not presently seem to understand. As I said at the meeting, in such a scenario the UK would have a new role in the global trading system. We would ourselves be traded. As the famous saying in Brussels goes, if you are not at the table, you are on the menu.”

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By making the case against a customs union to Conservative MPs, Fox also appears to be daring them to vote against any deal struck by May and Labour that includes such an arrangement.

At the same time, Leadsom, the leader of the Commons, called for May to consider asking for changes to her deal with the EU when she meets Angela Merkel, the German chancellor, in Berlin on Tuesday.

This option has been repeatedly ruled out by both the prime minister and EU leaders. However, Leadsom said she believed there was still hope that the EU could be persuaded to put a time limit on the Irish backstop arrangement, which otherwise potentially binds the UK into a customs union indefinitely.

“What I think would be fantastic is if Angela Merkel would try to support a proper UK Brexit by agreeing to reopen the withdrawal agreement,” she told Sky News. “As the person with the responsibility to get the legislation through, if we could get the PM’s deal over the line because the EU have decided to support measures on the backstop, then that would be the best possible outcome.”

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May is due to meet the German chancellor and the French president, Emmanuel Macron, on the eve of an emergency EU summit on the UK’s extension to article 50. She is likely to make the case for a short extension to article 50, until 30 June, but the most likely option to be offered by EU leaders is a longer one of up to a year, with the possibility of a break clause if a deal is passed in the meantime.

While May is in Berlin and Paris, talks between Labour and the government will continue at ministerial level, although sources said they remain at an “exploratory stage” and the two sides are “still a long way apart” on the main issues. The key areas that Labour wants to talk about are a customs union, a way to stop a successor to May unpicking the agreement and the possibility of a confirmatory referendum.

The chancellor, Philip Hammond, and the shadow chancellor, John McDonnell, were expected to join the discussions on Tuesday, as well as other key figures such as Michael Gove, the environment secretary, a leading Brexit supporter.

McDonnell said a second referendum could form part of the discussions. “What we are trying to do is ensure that we arrive at a deal which protects jobs and the economy. We don’t think Theresa May’s deal does that and we are also discussing the issue that she’s raised in cabinet about the issue of going back to the people,” he told ITV.

He said May had not moved on any of her red lines so far, “but we are trying to be as constructive as we can … We will broaden the talks out today to try and move them on.”

The justice secretary, David Gauke, denied the prime minister had suggested the possibility of a free vote on a second referendum in parliament – reportedly floated by May at a separate meeting with cabinet ministers – but said it was inevitable the issue would be brought to parliament again.

“As and when we bring a withdrawal agreement bill through the House of Commons … someone will bring an amendment on whether there should be a confirmatory referendum,” he said.

Campaigners for a second referendum are holding a rally in Westminster on Tuesday afternoon, with speakers including the Tory MP Huw Merriman, a parliamentary aide to Hammond.

Merriman has said he expects to be sacked for speaking at the People’s Vote rally. He said he had been angered by attempts to dissuade him from voting in favour of a referendum during the indicative votes process, despite having been assured it was a free vote.

He told BBC Radio 4’s Today programme: “It would be nonsensical for me to be given a free vote, to be allowed to vote the way I wish to vote, but then to explain I would lose my position. That’s the politics of the madhouse and I am just not willing to go along with that.”