But in a joint article for the Sunday Telegraph, they agreed that any transition would be "time limited" and that Brexit would mean the United Kingdom pulling out of both the EU single market and the customs union.
The British government is fighting back against criticisms that it is divided and unprepared for Brexit.
They said a "time-limited" transition period would "further our national interest and give business greater certainty" - but warned it would not stop Brexit. Hammond, who campaigned to remain in the European Union prior to last June's vote, has publicly made clear that he favours a softer Brexit numerous times, and is believed to have frequently clashed with May over her approach to leaving the bloc.
Mr Davis' Brexit department said it was preparing to publish several papers, including plans for a new customs arrangement and a proposal on how to resolve the difficulties of a non-physical border between Ireland and Northern Ireland.
"But we are also clear that during this period our borders must continue to operate smoothly; goods bought on the internet must still cross borders; businesses must still be able to supply their customers across the European Union and our innovative, world-leading companies must be able to hire the talent they need, including from within the EU". That means businesses need to have confidence that there will not be a cliff-edge when we leave the European Union in just over 20 months' time.
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.
Burnley stun nine-man Chelsea, Aguero downs Brighton
NAN also reports that Wayne Rooney scored the winning goal on his top-flight return to Everton after 13 years. As for the transfer market, the club is trying to do the best.
Mr Hammond has raised the prospect of a Brexit deal that saw little immediate change on issues such as immigration - something Brexiteers have rejected.
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".
Mr Miliband also described Brexit as an "unparalleled act of economic self-harm".
"The referendum will be no excuse if the country is driven off a cliff".
The EU bloc's chief negotiator, Michel Barnier, said last month there was "a clock ticking" on the Brexit talks.
The next round of talks is due at the end of the month, with both sides looking for progress towards a solution to three of Brexit's thorniest problems: how much Britain should pay to leave, what rights British and European Union citizens will have, and how to manage a land border to the bloc in Ireland.