The Brexit sub-committee gathers at Chequers with the government under pressure to spell out in detail what it wants to secure from Brexit talks.
The real test, however, will come when May's team put their demands to the EU. Offering little insight into how or whether the rifts that have hobbled talks to unravel more than 40 years of union had been healed, her office said her team had spoken for eight hours on subjects ranging from the vehicle sector to digital trade.
The letter adds to an increasingly divisive and angry debate over Britain's future relationship with the EU.
Mrs May will set out the Brexit agenda in a major speech next week following a meeting of the full Cabinet.
The report says that the European Union should be pragmatic about the terms of the UK's continued participation in its framework programmes, noting that Israel's agreement, for example, does not include freedom of movement.
Hunt, the health secretary, wasn't present at the gathering of May's Brexit strategy group but was sent onto the radio to brief the world on what happened.
"We will, as a sovereign power, have the right to choose to diverge", Hunt said.
Britain could also end up tied to new European Union spending programmes such as the Common Agricultural Policy without having a say over how they are designed or spent once Brussels' new long-term budget comes into effect on January 1 2021. But it seems likely now that there will be a transition period that will help both parties negotiate and transition to an equitable settlement.
The European Union should use Brexit as an opportunity to forge a stronger European research area which includes the United Kingdom and other countries outside the bloc, according to a leading charity.
Slides published online by the commission say such an approach would be "not compatible with the principles" set out in the EU's own guidelines and posed a risk to the "proper functioning" of its single market.
Labour leader Jeremy Corbyn is also to unveil a competing vision of how Brexit should work in what is being billed as a significant address on Monday, after some backbenchers called for more clarity from the leadership.
The customs union is at the heart of contention over the UK's position, with those who backed Remain wishing the country to remain within the existing union, or at least a newly constructed union that has some of the benefits.
The EU wants May to clarify how she sees Britain's future relationship with the bloc.