Boris Johnson, the man likely to enter Number 10 next week, was given a fresh warning of the challenges he will face as Mr Hammond promised to do “everything in my power” to block a no-deal.
The Chancellor left open the possibility of voting to bring down a Conservative government led by Mr Johnson if the UK was on course to crash out of the EU without a deal on 31 October.
In interviews with German and French newspapers, Mr Hammond warned EU leaders that “some are trying to make the Europeans so tired that they ask us to leave... but please, do not listen to the few noise-makers.”
Mr Johnson has again ruled out seeking an extension to the deadline, insisting that the UK would leave the EU on Halloween “come what may”.
But Mr Hammond said it would be impossible to renegotiate a deal with Brussels before that deadline.
Speaking to Le Monde and Suddeutsche Zeitung, he said: “I will take steps to avoid an exit without agreement apart from an explicit parliamentary approval. There should be a new and sincere attempt to reach a consensus.”
Hinting at the prospect of another referendum, he said: “If we do not find a solution with the members, we may have to ask the British to give their opinion again, in one form or another.”
Asked again to rule out supporting a motion of no confidence, the Chancellor said: “I do not exclude anything for the moment.”
On Thursday, MPs voted by a majority of 41 to back a measure aimed at preventing Mr Johnson suspending Parliament in order to force through a no-deal Brexit, with 17 Tories rebelling and dozens more abstaining.
The Chancellor, Justice Secretary David Gauke, Business Secretary Greg Clark and International Development Secretary Rory Stewart did not vote. All are expected to oppose a no-deal Brexit from the backbenches.
Another frontbencher, Health Minister Stephen Hammond, signalled on Friday that he too would be willing to vote down a Johnson administration in a no-confidence vote if it pursued a no-deal exit.
Asked whether he was prepared to press the “nuclear button” with such a vote, he repeatedly cited putting the national interest before personal ambitions.
“I hope we never get there, but I think a lot of people were taught that you must put the interest of the country before yourself,” he told the Today programme.
Tory Eurosceptic Jacob Rees-Mogg poured cold water on the significance of the Commons vote aimed at preventing the new prime minister suspending Parliament.
“Something that was never going to happen is now slightly harder to do,” he said.
The Tory MP also suggested the likelihood of a successful no-confidence vote was slim, accusing MPs of trying to “bluff” their way to preventing Brexit.
“It’s quite difficult unless they have a vote of no confidence and they don’t want to do that because they would lose their seats... any Conservatives who voted against the government on a vote of no confidence would be automatically deprived of the whip.”
The French government urged Britain to sign up to Brexit deal, with Europe minister Amelie de Montchalin using a visit to the Irish border on Friday to say it was a “necessity” to preserve the peace process. Her Irish counterpart, Helen McEntee, said checks following a no-deal Brexit would be “sub-optimal” to agreeing the backstop.