The comments by the Chancellor at an event in Davos caused fury among Eurosceptics, who accuse him of fighting a rearguard action to soften Brexit.
Mr Hammond said the approach to Brexit would not be swayed by Tory rebels on either side of the European Union divide.
"It's a fact our economies are integrated, that's the baseline from which we leave the single market and customs union - which clearly represents change", he said on Twitter.
People who objected to his approach were disrespecting the thinking behind British voters' June 2016 decision to leave the EU, Hammond said.
Dozens of MPs are said to have sent letters to the powerful backbench 1922 Committee, with speculation that numbers are coming close to the 48 needed to trigger a full ballot.
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Jacob Rees-Mogg MP speaking to supporters during a Conservative Voice meeting, in the Boothroyd Room at Portcullis House, London..
The duration of the transition or implementation period would be strictly limited and last about two years, it added. "This is no way to negotiate and it is no way for this country to behave", he said.
"Participating in a customs union should not preclude us from formally negotiating - or indeed signing - trade agreements", he will say on Friday.
He warned May and her cabinet colleagues against allowing Brexit to become "only a damage limitation exercise".
In the longer-term, he said, the US currency's value will be determined by the underlying strength of the USA economy. "They did not vote for the management of decline", he said in a speech Thursday, accusing ministers of being "timid".
"The negotiations that are about to begin sound as if they aim to keep us in a similar system to the single market and the customs union", Rees-Mogg said.
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South Korean military officials also have said the drills would resume but it's too soon to disclose the exact date and size. The United States banned the transfer of refined oil products to and from North Korea in August of previous year .
I'm told that Mr Davis will acknowledge there has to be some kind of process, mechanism, or cunning wheeze, where the United Kingdom can make sure it is still in the room when decisions are made, even if technically we have lost all rights to do so.
All of which might, it seems, come as quite a shock to many people in Britain who appear to have been comforting themselves, of late, with the idea that Brexit will never really happen; or that if it does, it will come in a form that can be sold to voters as Brexit, but will in fact be nearly unnoticeable.
He said that leaving the European Union would ultimately lead to "lower prices for everyday products" because of Britain's withdrawal of the Common External Tariff, helping more "disadvantaged" Britons. First it's looking to agree on a transition period after Brexit in March 2019 that make the exit less abrupt.
However, Davis used his speech today, in Middlesbrough, North East England, to paint an optimistic portrait of Britain's trading opportunities after Brexit.
While negotiations between London and Brussels regarding the new regulations during the transition period which would take place in two years have started last June and is expected to end in March next year.
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Asked Wednesday if he was interested in seeing the document, Cornyn said "sure" and chuckled. If he objects, the full House would meet privately for a vote to decide the matter.