The international development secretary’s comments mark a change in stance from the previous “no deal is better than a bad deal” line, taken by Theresa May since early 2017.
The comments from Dr Fox, who has been seen as a leading Brexiteer, come as the prime minister appeared to have at least temporarily stemmed the flow of resignations from her front bench that began on Thursday.
Claims that there were also now enough letters from Tory MPs calling for Ms May to resign were also being called into question on Friday, with a vote of no confidence looking unlikely until next week.
In a message apparently aimed at rebel MPs, Dr Fox said: “I hope that we all take a rational and reasonable view of this. We are not elected to do what we want, we are elected to do what’s in the national interest.
“Ultimately I hope that across parliament we recognise that a deal is better than no deal. Businesses do require certainty, confidence as they go forward for their planning.
“And there are those round the world who are waiting to get certainty also to begin to discuss trade agreements with the United Kingdom. It is in our national interest.”
Catherine Stihler, Labour MEP and Best for Britain champion, said the comments served to underline why there is need for new referendum on Brexit.
She went on: “This is a rebuke to the hardline Brexiteers who want to push Britain over the cliff-edge. It demonstrates the extent of the civil war engulfing the Tory Party.
“A no-deal scenario would undoubtedly be more calamitous than a deal approved by EU member states, costing hundreds of thousands of jobs. But there is no such thing as a good Brexit deal. The only way to protect jobs and grow our economy is as part of the EU.”
Ms May’s defacto deputy David Lidington also hit the airwaves to tel Tories plotting against her they should instead rally behind the Prime Minister in the “national interest”.
Cabinet Office minister praised Ms May’s resilience in carrying out the “absolutely back-breaking job” of delivering a Brexit deal for the United Kingdom.
Earlier in the day it emerged that environment secretary Michael Gove was now not likely to quit, amid speculation that he would follow Dominic Raab and Esther McVey in resigning over the draft Brexit plan.
Former Brexit minister Steve Baker – a leading member of the European Research Group which is at the forefront of attempts to now depose Ms May – said he believed they were close to getting the 48 letters of no confidence needed to trigger a vote on her future.
“People have been ringing me and they are telling me that they are putting letters in. I have spoken to colleagues as well and I think we are probably not far off. I think it is probably imminent,” he told BBC2’s Politics Live.
He acknowledged he had sent a WhatsApp message to colleagues earlier saying that his count was over 48, with around a dozen probables, but admitted the number was probably inaccurate.
He said that only Sir Graham Brady, chairman of the 1922 Committee, knew the true figure.
Mr Baker added: “My number will be inaccurate because people will withdraw letters, they will tell me they have put letters in when they haven’t, they will take them out and not tell you they have taken them out.”