Asked what he would do if the Brexit plan ended up limiting Britain's ability to conduct trade deals with non-EU countries, Fox said: "I don't believe it does".
Mrs May gathered her new team at 10 Downing Street as shockwaves continued to reverberate in Westminster following the first day since 1982 when two Cabinet ministers resigned within 24 hours.
Will Theresa May face a leadership challenge before the Conservative party conference in October?
The trans-Atlantic relationship has had some awkward moments since Trump's election.
A third amendment would require the government to sign up to having a separate Value-Added Tax regime from the EU, while a fourth would oblige the PM to creating primary legislation if she wanted to remain in the EU's customs union.
While British Prime Minister Theresa May might have hoped her meeting with U.S. President Donald Trump Friday could draw a line under the spate of resignations she suffered early in the week, it is likely to only further expose her weakness and divided leadership. And I maybe well speak to him when I get over there.
Brexit betrayed or the end of May: What does David Davis's resignation mean?
He was enthusiastic about Johnson, calling him "a friend of mine".
Fast-forward a few days and Brexit hardliners are on the defensive, while the government is showing a willingness to compromise and outlining a more pragmatic vision for a country half-in, half-out of the European Union. Mr. Johnson was quickly replaced by 51-year-old former Health Minister Jeremy Hunt, who unlike Mr. Johnson supported staying in the European Union in the 2016 referendum.
But his claims were dismissed by former defence secretary Sir Michael Fallon, who said: "Dreaming is good, probably for all of us, but we have to deal with the real world".
The latest blow came as the media in London reported that one Conservative member of parliament (MP) has submitted a formal letter calling for a confidence vote in May as the leader of the party. The Conservatives now have 316 MPs so 48 of them would need to write such letters to challenge May.
The ex-MP said there was a "plan" to curtail the role of the Brexit department.
The two resignations have left May badly exposed and raised questions over whether she will stand firm in her commitment to pursuing a "business-friendly" Brexit, or will be faced with more resignations and calls to quit herself.
In a policy paper, the government will outline proposals to allow Britain to maintain close economic and security ties with the European Union even after it leaves the bloc in March.
"Our priority around Brexit is to ensure that Australia secures a free trade agreement with the United Kingdom that's as beneficial to both countries as possible, as soon as possible", Mr Pyne said.
Four out of five readers who took part in our survey said the Brexiteer big beasts were right to quit the Cabinet, a move which has been widely praised by many of those to the right of the Tory party.