Britain's Brexit Secretary David Davis was expected to spell out on Friday London's aims for the next round of negotiation with Brussels, which both sides want to result in a provisional agreement by March that will ease business concerns about what will happen once Britain is out of the European Union on March 30, 2019.
Mr Rees-Mogg, chairman of the influential European Research Group, was warning that close alignment with the EU after Brexit would prevent "meaningful" trade deals with other countries, leaving Britain a "vassal" of the remaining 27-nation bloc.
Davis said in a speech outlining his view of a post-Brexit transition on Friday that he expected to start talks in the coming "days and weeks".
In a speech delivered at the World Economic Forum in Davos on January 26, Davis said he, the Prime Minister and the Chancellor all wanted the United Kingdom exit to serve both businesses and the British people. "The aim then on the part of the commission would be to spin out the negotiation", he told the committee.
"There are people on both sides of this argument who do not support us in our intention to deliver the Brexit that the British people have mandated in a pragmatic way that protects British businesses and British jobs", he said.
Former Conservative MP Lord Forsyth told the BBC's Question Time Mr Hammond had appeared to "say something that's completely at odds with what the prime minister said in her Lancaster House speech" - in which she set out the UK's strategy for Brexit.
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Any such deals would enter into force at the end of the implementation period.
Health Secretary Jeremy Hunt said it was "absolutely wrong" to accuse Mrs May of a "timid" approach to Brexit.
"This is the Prime Minister that gave us absolute clarity after the Brexit vote that we were going to get back control of our laws, our borders, our money - the most profound strategic decision any prime minister has to make in the current circumstances".
The febrile mood in the party is likely to linger for May, who has struggled to keep her divided lawmakers united over everything from transition, to the future relationship, to the so-called Brexit dividend - the funds that will be freed up when Britain stops paying into European Union coffers.
The PM has already made clear that we will broadly accept the existing rules and regulations, and ministers agree that although we will officially be outside the single market free trade area and the customs union, we'll replicate those arrangements so that industry isn't dealing with dramatic overnight change.
Speaking in Davos, the Chancellor enraged hard Brexit supporters with his support for only "very modest" changes to the UK's trading rules with the European Union, setting out the risks of trying to break free.
Furious Tory MPs threatened to oppose Government Brexit legislation in protest in the latest threat to Theresa May's dwindling authority.