Tory Brexit tensions have heightened after Chancellor Philip Hammond and Home Secretary Amber Rudd committed to transitional arrangements after the UK leaves the bloc in March 2019.
However, International Trade Secretary and leading Brexiteer Liam Fox said unregulated free movement of labour after Brexit would “not keep faith” with the EU referendum result and that the Cabinet had not agreed a stance on immigration.
Mr Hunt told the BBC he “didn’t recognise this picture” of Cabinet splits over Brexit, adding there was unity on delivering a Brexit that restores control over Britain’s laws, borders and money.
Speaking on the Today programme, he added: “If you look at where we are now compared to where we were a few months ago, we’ve sent some very positive messages to Brussels about what we want.
“The other thing that we are completely united on as a Cabinet is that we want Brexit to make Britain more global, and not more insular.
“That means that it has to be a Brexit that works for business, it has to work for the NHS, the NHS needs to recruit doctors and nurses from all over Europe and that is going to continue after we leave the European Union.”
Brexit “excites huge passions”, Mr Hunt said, with Cabinet ministers on different sides of the argument.
He added: “We’re not going to have a cliff-edge, but what we have said is that the implementation period must be complete by the time of the next election.”
Mr Hunt said this implementation would be complete “at the latest” three years after Britain leaves the EU, adding: “It could happen earlier than then, but we want to make sure that businesses, NHS hospitals, everyone can carry on recruiting the people they need to continue to give the services that they offer.”
Liberal Democrat leader Sir Vince Cable said the Cabinet had descended into “civil war” on the issue, as he referred to rumours Foreign Secretary Boris Johnson may resign over whether a three-year post-Brexit transitional scheme for migrants would come into force.
A spokesman for Mr Johnson said: “Vince Cable is making this stuff up and maybe he should take more time to think up some policies rather than wasting his time on peddling lies.”
The clash came after Mr Hammond used an interview with Le Monde to downplay claims Britain could try to become a Singapore-style low tax economy if it does not get the Brexit deal it wants.
He said: “I often hear it said that the UK is considering participating in unfair competition in regulation and tax.
“That is neither our plan nor our vision for the future. The amount of tax we raise as a percentage of our GDP puts us right in the middle of the pack.
“We don’t want that to change, even after we’ve left the EU.
“I would expect us to remain a country with a social, economic and cultural model that is recognisably European.”
Peter Dowd, Labour’s shadow chief secretary to the Treasury, said: “This Government has broken down into farce.
“The Chancellor is not only disagreeing with Cabinet colleagues over Brexit, he is now in open dispute with himself given it is only his own comments on the matter in January which he is pretending to contradict.
“The truth is that the British people will not believe the fake U-turn of a Tory Chancellor in a French newspaper, while he is still going ahead with billions of pounds in corporation tax giveaways in this parliament, and refuses to rule out further cuts.”
Defence Secretary Sir Michael Fallon said the issue of immigration policy during a transitional deal would be “one of the details” for the Brexit negotiations.
Sir Michael, taking part in Passchendaele memorial events in Ypres, insisted there was not an “argument raging” within the Cabinet on the issue.
He said: “It’s not an argument, it’s part of the negotiations. We have always understood that we have to ensure immigration is managed properly, that’s what the public expect to see - that there are controls of it.
“That’s one of the details that’s going to be sorted out during the negotiations. It’s not an argument raging around the Cabinet table.”