The Foreign Secretary is said to have made clear in private that he is against any agreement that would tie Britain to a form of customs union with no clear way to leave in future.
Eyebrows were raised when Mr Hunt attended a pizza night hosted by senior Brexiteer Andrea Leadsom, the Commons Leader, in her office at the Commons.
A third of the Cabinet turned up and ate through three large sized takeaway pizzas - a margherita, a hot & spicy, and a vegetarian - plus crisps and dips, washed down with red and white wine.
Ms Leadsom holds regular such meetings with fellow Brexiteers but it was the first time that Mr Hunt had attended.
A source said Mr Hunt appeared “genuinely concerned about us getting locked in” without a clear way out.
Others present were Treasury Chief Secretary Liz Truss, Brexit Secretary Dominic Raab, Attorney General Sir Geoffrey Cox, Environment Secretary Michael Gove, International Development Secretary Penny Mordaunt, Transport Secretary Chris Grayling.
Apologies were received from International Trade Secretary Liam Fox, Home Secretary Sajid Javid, Lords leader Baroness Evans, Secretary Matt Hancock and Work and Pensions Secretary Esther McVey.
Mr Hunt’s position emerged as Theresa May moved to avoid a confrontation with ministers at today’s Cabinet by abandoning plans that could have kept Northern Ireland aligned with the EU for an indefinite period.
Germany angrily turned up the heat on the Prime Minister, with Europe Minister, Michael Roth calling on her to “take responsibility and be constructive” as he arrived for talks in Berlin.
Earlier Mr Roth told the BBC that Brexit would be “painful” and suggested the November summit planned to seal a deal might be used to plan “a disorderly no-deal Brexit” instead.
“We are not bargaining at a cattle market here,” he said. “We the EU are not going to allow ourselves to be blackmailed.”
Mrs May’s Democratic Unionist Party allies said they could “paralyse” her Government if she fails to protest Northern Ireland’s position within the UK in the Brexit negotiations
Downing Street adopted a relaxed attitude to the pizza evening.
“Cabinet ministers are free to eat whatever they choose,” said the PM’s spokesman beforehand. “Cabinet colleagues have discussions with each other all the time.”
European Council President Donald Tusk said that while there was goodwill on both sides, the negotiations have been more complicated than expected and Britain was “more likely than ever before” to crash out of the EU without a deal. urged not to give up. No deal expected this week.