But initial reactions from across the English Channel suggested France and Germany were digging in too.
EU leaders and May have said they want to get a deal agreed in October, to be finalised in November.
In Paris, Minister for European Affairs Nathalie Loiseau said that, while France still believed a good Brexit deal was possible, it must also prepare for a 'no deal' outcome.
Britain's vote to leave "cannot lead to the EU going bust," she said on France Info radio. "...That's the message we have tried to send for several months now to our British counterparts, who may have thought we were going to say 'yes' to whatever deal they came up with."
In Berlin, German Deputy Foreign Minister Michael Roth said the other 27 EU states were striving to achieve reasonable solutions. "The blame game against the EU is therefore more than unfair. We can't solve the problems that are arising on the island (Britain) due to Brexit," he said on Twitter.
In London, the Telegraph reported that May faced the prospect of ministerial resignations next week if she failed to come up with an alternative to the "Chequers" Brexit plan that she presented in Austria.
After May's Friday statement, European Council President Donald Tusk said that the results of the EU's analysis of that plan had been known to Britain for many weeks. But Hunt said there was a difference between rhetoric and substance.
"On the substance of the Chequers proposals, we have not had a detailed response," he said, adding that EU proposals for the Irish border would mean that it was impossible "to leave the EU intact as one country".
Hunt also said Britain's economy would be able to withstand a no-deal Brexit, saying it was "absolutely right" that many Britons were now content to leave the EU without a deal.
Around 52 percent of Britons voted to leave the EU in a referendum in 2016 and 48 percent to stay.
"Even in a situation where we aren't able to come to an agreement, we would be trading on World Trade Organisation terms. It would be bumpy, it would be difficult, but we would find a way to survive and prosper as a country," Hunt said.
"We've had far bigger challenges in our history. But it's not our desired outcome."
In Berlin, magazine Der Spiegel said Germany's government expected the impact of a no-deal Brexit on its labour market to be "relatively small". It cited a government response to a request for information from the far-left Linke party.
