The ministers were seen being on opposing sides on Brexit, with Hammond championing a business-friendly approach where Britain gradually leaves the European Union while Fox sought as short a transition as possible, and for Britain to have the freedom to immediately negotiate trade deals.
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".
Philip Hammond and Liam Fox have poured cold water on the idea of a soft Brexit by declaring Britain will not remain in the single market or customs union.
"That is why we believe a time-limited interim period will be important to further our national interest and give business greater certainty - but it can not be indefinite; it can not be a back door to staying in the EU", Mr Hammond and Mr Fox wrote.
The old divisions in the Tory party over Europe appeared to resurface when Mr Fox said that any such transition period would end before the next general election in 2022.
"We will leave the customs union and be free to negotiate the best trade deals around the world as an independent, open, trading nation", the ministers said, adding that the government was committed to make sure there "will not be a cliff-edge when we leave the EU in just over 20 months' time". "And has that moment arrived yet?" she wrote in an article for The Mail on Sunday.
Meanwhile, the leading Conservative Remainer Anna Soubry indicated she could be prepared to join with politicians from other parties to stop the country "staggering recklessly" towards a hard break with Brussels.
"The answer to the first question is "it is not impossible"; the answer to the second is "no".
Brexit Secretary David Davis said exactly how the transitional arrangements would work had still to be determined.
Officials said the papers would show the British government was ready to "broaden out" the negotiations and move forward towards a deal that worked for both sides.
In July, British Foreign Secretary Boris Johnson criticized the European Union over Brussels' demand for a Brexit divorce bill, saying, "The sums I have seen that they propose to demand from this country appear to be extortionate".
Philip Hammond has been accused of ceding ground to cabinet Brexiters on Sunday after adding his signature to an article saying the United Kingdom would not remain in the customs union framework during the transitional period after Brexit. He described the outcome of last year's referendum as an "unparalleled act of economic self-harm".