In a joint 'Sunday Telegraph' article, UK Chancellor Philip Hammond and international trade minister Liam Fox - the two key ministers believed to be on opposing ends of Britain's future outside the EU - also said that the UK will not remain in the customs union during the transitional period.
"We are both clear that during this period the UK will be outside the single market and outside the customs union and will be a 'third-country' not party to EU treaties," they wrote.
They said the UK's borders "must continue to operate smoothly", that goods bought on the Internet "must still cross borders", and "businesses must still be able to supply their customers across the EU" in the weeks and months after Brexit.
The two leading politicians said the government wanted to ensure "there will not be a cliff-edge when we leave the EU".
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In their article, Hammond and Fox said: "We respect the will of the British people - in March 2019 the United Kingdom will leave the European Union.
"We will leave the single market, because there was a vote for change on June 23rd and that is what we will deliver. We want our economy to remain strong and vibrant through this period of change. That means businesses need to have confidence that there will not be a cliff-edge when we leave the EU in just over 20 months' time.
"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 cannot be indefinite; it cannot be a back door to staying in the EU."
Meanwhile, former Labour foreign secretary David Miliband has called for politicians on all sides to unite to fight back against the "worst consequences" of Brexit. He described the outcome of last year's referendum as an "unparalleled act of economic self-harm".
Writing in the 'Observer', he said: "People say we must respect the referendum. We should. But democracy did not end on June 23 last year.
Negotiations between Brexit Secretary David Davis and EU officials are set to resume at the end of this month.
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