Foreign Secretary Jeremy Hunt has warned Theresa May against agreeing a Brexit deal with Labour that involves a customs union with the EU.
Mr Hunt suggested that such an agreement would result in even fewer Tory MPs backing a deal in Parliament.
But Jeremy Corbyn insists his support is contingent on ministers accepting the need for a customs union.
Supporters say it would be better for businesses, but opponents feel it stops the UK setting its own trade policy.
All EU members – including the UK at present – are inside the customs union, meaning they do not have to pay taxes, called tariffs, to move goods and services between them.
This keeps cost down and avoids delays, but members have to operate as part of a bloc and cannot do their own trade deals with other countries around the world.
Labour is arguing for the UK to be part of a new form of customs union arrangement where the country could have “a say” in policy despite no longer being in the EU.
Critics say the EU would never agree to that, and in any case, the purpose of Brexit is to break free and remaining in a customs arrangement would go against that.
Leaving the customs union was also a Conservative manifesto commitment at the 2017 general election.
Talks between Labour and the government have been taking place for a number of weeks after Mrs May’s Brexit deal with the EU was effectively rejected for a third time by MPs.
Labour has previously complained that the government appeared unwilling to move on a number of key areas, particularly on the possibility of a customs union.
But the PM’s de facto deputy David Lidington said on Monday that the latest round of talks had been “productive”, while Labour described them as “constructive”.
However, Mr Hunt told BBC Radio 4’s Today programme: “If we were proposing – which I very much hope we don’t – to sign up to the customs union, then I think there is a risk you would lose more Conservative MPs than you would gain Labour MPs.”
However, he said he “definitely” thought the government could secure a deal that MPs would back.
Other cabinet ministers – including International Trade Secretary Liam Fox – have also recently signalled their unease at a customs union agreement.
But Nick Boles, an independent MP who quit the Conservatives over the party’s Brexit stance, criticised Mr Hunt’s comments as “ignorant and unhelpful”, saying on Twitter that it revealed “naked opportunism” over the Conservative leadership.
Mrs May has said she will resign if her deal is passed through Parliament, leading to the prospect of an imminent leadership contest.
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Ministers insist it is still their aim to get MPs’ approval for the terms of the UK’s exit from the EU by 22 May so the country does not have to take part in elections to the European Parliament a day later.
To that end, No 10 says it wants to introduce the Withdrawal Bill – legislation required to implement the withdrawal deal – to Parliament as soon as possible, but Downing Street said that process would not begin until it had a “realistic prospect of securing passage”.