It has confirmed it will publish a number of papers, including one on Northern Ireland's border and future customs arrangements.
"We will leave the customs union and be free to negotiate the best trade deals around the world as an independent, open, trading nation", Hammond and Fox wrote in the Sunday Telegraph newspaper.
The statement, by the ministers seen as representing the opposing visions of Brexit in Prime Minister Theresa May's cabinet, confirmed the government will be pushing for a period of transition so businesses can avoid a "cliff edge".
That will come alongside other documents setting out how Britain's involvement in the customs union with other EU countries this week.
"I've launched this process because with time of the essence, we need to get on with negotiating the bigger issues around our future partnership to ensure we get a deal that delivers a strong United Kingdom and a strong EU", Mr Davis said.
"We will leave the single market, because there was a vote for change on June 23rd and that is what we will deliver".
"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 European Union". Irish Prime Minister Leo Varadkar said last week that Brexit advocates "already had 14 months" to issue detailed proposals, but had not.
The UK government is to publish a series of Brexit strategy papers starting from this week, ahead of a third round of talks between London and Brussels at the end of August.
In the coming week the British government is to begin publishing papers that will have more details of its policies and goals in relation to the Brexit process.
Mr Miliband, who narrowly lost out to his brother Ed in the 2010 Labour leadership contest and who now heads the International Rescue Committee relief agency in NY, described the outcome of the 2016 referendum as an "unparalleled act of economic self-harm".
'Our security and police services are working together because terrorists and criminals don't respect national borders, ' Mr Verhofstadt said.
In recent weeks, the Taoiseach has made plain his growing frustration with Britain's failure to come up with workable proposals in the 14 months since last year's European Union referendum.
"The referendum will be no excuse if the country is driven off a cliff", he declared.
Brexit Secretary David Davis is to hold a third round of talks with the EU's chief negotiator, Michel Barnier, in Brussels at the end of the month.