The International Trade Secretary said that while the Government wanted a deal, Brussels had to know that the UK would be prepared to walk away without an agreement.
Dr Fox said Prime Minister Theresa May was “likely” to remain in Number 10 throughout the current parliament and warned that speculation about leadership would distract from the “historic” task of Brexit.
Mrs May has repeatedly stated that her approach to Brexit was “no deal is better than a bad deal” and Dr Fox said it was important that the EU recognised that resolve.
He told BBC Radio 4’s Today: “We don’t want to have ‘no deal’, it is much better that we have a deal than no deal. We can of course survive with no deal and we have to go into a negotiation with those on the other side knowing that’s what we think.
“But of course we want to come to a full and comprehensive deal with the European Union.”
Such a deal would benefit both the UK and EU and “the only reason we would not come to a free and open agreement is because politics get in the way of economics”.
Dr Fox stressed that leaving the EU meant quitting the single market and customs union as he was pressed over whether the UK could stay inside those arrangements as part of a transitional deal.
“If we are to have an implementation phase between leaving the European Union and our final settlement, I don’t have a problem with that.
“But I do think we have to leave the EU first of all to keep faith with the voters who instructed us to do that.”
He added: “You cannot leave the European Union and be in the single market or the customs union.”
Mrs May has issued a warning to her Cabinet ministers that none of them is “unsackable” after she was forced to upbraid senior colleagues following an outbreak of vicious briefing against Chancellor Philip Hammond.
Asked if he was confident of still being in his position in a year’s time, Dr Fox said: “I wouldn’t predict anything in the future, in politics you never know what’s going to happen next.”
He added: “In terms of the Prime Minister, I think that the Prime Minister is likely to be there for the rest of this parliament.”
She has a mandate and the support of colleagues, he said, adding: “I don’t think there is anything to be gained by speculation about leadership. We have got a job to do, we have got a very big task, a historic task, and that is what we should concentrate on and to be diverted into personality issues I think doesn’t either do the Conservative Party, the Government or the country any good.”
Dr Fox was using a visit to Geneva to meet World Trade Organisation (WTO) director general Roberto Azevedo to discuss the UK’s post-Brexit arrangements and to deliver a speech pushing for a rejection of protectionism.
He said methods other than free trade agreements could be used to liberalise global trade and the UK would use its seat on the WTO after Brexit to “shape the debate”.
The debate around free-trade agreements “is too narrow and we need to think about new ways of getting the global economy moving”.
The UK is seeking to replicate its current EU trade obligations at the WTO as it takes a seat in its own right after Brexit and Dr Fox said the organisation was “very positive” about the process.