Jeremy Hunt has said there is no possibility of the government backing a customs union with the EU after Brexit.
The health secretary said the UK wanted "frictionless trade" but would "find a different way" to achieve that.
A Conservative MP says she has cross-party support for an amendment calling for the government to form "a" customs union with the EU after Brexit.
Theresa May will make a speech on the UK's future relationship with the EU next Friday.
And Labour Leader Jeremy Corbyn is set to outline Labour policy on a customs union on Monday, amid reports that his party's position on it is "evolving".
If he backs membership of a customs union, it could mean Mrs May faces a Commons showdown over the issue - with pro-European Conservative rebels joining forces with Labour MPs.
Conservative MP Anna Soubry says she has cross-party support for an amendment to the Trade Bill, currently going through Parliament, urging the government to pursue as a negotiating objective forming a customs union after Brexit.
A customs union means countries club together and agree to apply the same tariffs to goods from outside the union - but it does not allow members to strike their own trade deals.
Jeremy Hunt told BBC Radio 4's Today programme a customs union was "one way of getting frictionless trade but it is not the only way".
The government wanted to agree "frictionless trade by agreement between two sovereign bodies, the United Kingdom and the European Union", he said.
Asked if there was any possibility of the government coming round to the idea of a customs union with the EU after Brexit, he replied: "No".
The health secretary was not at the meeting of senior ministers at Chequers on Thursday, at which the UK approach to Brexit was discussed over eight hours.
But he said he had been told there had been a "very positive discussion" and "good progress" had been made.
He said a broad agreement had been reached at Chequers, ahead of a discussion by the whole cabinet and the prime minister's speech next week.
"You have divergent views on a big issue like Brexit as you would expect - but the central common understanding is that there will be areas and sectors of industry where we agree to align our regulations with European regulations," he said.
"The automotive industry is perhaps an obvious example because of supply chains that are integrated.
"But it will be on a voluntary basis, we will as a sovereign power have the right to choose to diverge, and what we won't be doing is accepting changes in rules because the EU unilaterally chooses to make those changes."
Environment Secretary Michael Gove, who was at Chequers, told Sky News there had been "a very good atmosphere" while Home Secretary Amber Rudd told the BBC: "We all got behind the prime minister and we've agreed the basis for her speech next week and looking forward to it going ahead."
But pro-EU Labour backbencher Chuka Umunna - an ally of Anna Soubry - warned Theresa May her plan to leave the customs union could be defeated by MPs.
"There is no majority in the House of Commons for us not to participate in the customs union, that is absolutely clear... it's the reality of the parliamentary arithmetic."
Of the government, he said: "If they are not going to change their position they are going to lose votes in the House of Commons, it's a straightforward as that."
He said Labour's position had been "evolving" on staying in some form of customs union and he said he was confident his party would back the amendment put forward by him and Ms Soubry.
Meanwhile the Times has reported that the prime minister is planning a U-turn over the right of EU citizens who arrive in the UK after Brexit, but during the "transition period", to remain in the country permanently.
Conservative Brexiteer Jacob Rees-Mogg told the BBC that would be "quite wrong": "I'd be astonished if Mrs May would make U-turn of that kind; she is a lady of great backbone and for her to kowtow to the European Union is, I think, unconscionable."
http://www.bbc.co.uk/news/uk-politics-43167824