But in a joint article for The Sunday Telegraph newspaper, they agreed there should not be a "cliff-edge" when Britain leaves in March 2019.
Finance minister Philip Hammond, who favours a softer, pro-business Brexit, and International Trade Secretary Liam Fox, a hardline supporter of Britain leaving the European Union, have clashed over the UK's future outside the bloc.
They also underlined that Britain would operate outside the single market and customs union after Brexit.
From this week, the Government is to start publishing a new series of detailed papers setting out its negotiating position on a range of key issues, amid criticism from Brussels of a lack of clarity about what it wants.
"We will await publication of the full position paper before making further comment and trust that the Irish government will engage seriously and pragmatically in helping to secure an agreement that benefits everyone".
Vince Cable, the Lib Dem leader, said the article showed that it was not Hammond who "calls the shots" in the cabinet over Brexit.
"Over the summer, we heard that Philip Hammond was courageously fighting off the more extreme Brexiteers".
The government says it hopes to persuade the 27 other European Union nations to start negotiating a "deep and special" future relationship that would include a free trade deal between Britain and the EU. Supposedly he was looking for a compromise to keep Britain within the customs union and single market as long as possible. "He has now teamed up with one of the more extreme and ideological supporters of a hard Brexit".
The two ministers, who represent the Remain and Leave wings of the Tory party respectively, write that Britain will not stay in the European Union by the "back door".
The jointly penned article appeared created to reassure those in favour of a clean break, but will do little to comfort those fearing the consequences of a so-called "hard Brexit".
"Once the interim period is over, we want a permanent, treaty-based arrangement between the United Kingdom and the EU which supports the closest possible relationship with the European Union, retaining close ties of security, trade and commerce", Hammond and Fox said.
But they did not explain how these aims would be achieved.
Writing in the Mail on Sunday, Soubry said: "If the prime minister or her successor [in the event of May standing down] is not prepared to confront the ideologues, I gravely fear that the party could split - and that would change Britain's political landscape completely".