Prime Minister Theresa May has defended her Brexit plans.
Rebuffing claims that her proposals make too many concessions to the EU, May said her "smooth and orderly Brexit" would leave Britain free to make its own laws and trade deals.
"I think it is right that the cabinet backs the prime minister and speaks with one voice and if people don't do that then they have to go", Justice Secretary David Gauke told BBC radio.
All eyes are on Foreign Secretary Boris Johnson, who is due to speak at a diplomatic conference later on Monday, and Environment Secretary Michael Gove.
The British leader may have stilled the waters over a possible leadership contest, but some Conservative Brexit supporters are still incensed over what they see as her decision to break her promise for a clean break with the EU.
Despite this support from within her party, following the resignation of Mr Davis a poll by broadcaster Sky News has found that the British people have turned on her.
The Prime Minister used a lavish banquet at Blenheim Palace to tell him there was an "unprecedented" opportunity to do a deal that boosted jobs and growth in both countries.
He said trade agreements and some issues regarding the Ireland-Northern Ireland border need to be hammered out. Inside, the paper's report says May finds herself in a "serious crisis" caused by her "inability" to manage an orderly Brexit.
She also said that the government had no intention of extending Article 50, which is a notice of intention to leave the European Union, and that there will not be a second national vote on this Brexit deal. European Commission officials are meeting business groups to discuss the consequences of failing to reach an accord with the United Kingdom, a second person said, amid concern that companies aren't doing enough to prepare.
"I believe this will help the Government stick to the promises it made".
May has repeatedly ruled out another referendum, but about 100,000 supporters of the European Union marched through central London last month to demand that the British government hold a final public vote on the terms of Brexit.
They will hold talks at the Prime Minister's country residence of Chequers on Friday where Russia, Brexit and the Middle East will top the agenda. A "responsible government" has to prepare for a variety of outcomes in the negotiations, "including a no deal".
Mr Rees-Mogg - considered by some a favourite for leadership - expected Mrs May to remain at least until the official date of Brexit in March 2019.
Labour MP Andrew Adonis said Raab's appointment could spell the "death" of the Tory leader, while writer and editor Hitcham Yezza said Brexit has now become even more "shambolic".
A leadership challenge can be triggered if 15% of members of parliament in May's Conservative Party write a letter to the chairman of the party's so-called "1922 committee".