May said her plan still involves leaving the customs union and single market, "but supports shared prosperity and security" between Britain and the EU.
Juncker addressed the European Parliament at the start of a crucial week for British Prime Minister Theresa May who will gather her divided ministers on Friday to thrash out the trade ties Britain wants with the EU after Brexit.
Responding to Mr Rees-Mogg's comments, the Prime Minister's spokesman said: "Our focus is on delivering the will of the British people".
"The last thing we need is a leadership challenge", he said on Twitter.
Trump tweets that EPA chief Scott Pruitt has resigned
The president added that he has "no doubt that Andy will continue on with our great and lasting EPA agenda". Since then, he has lobbied for various energy industries, including the coal industries.
"I call on other rational members of the party to stand against this nonsense".
Downing Street was reportedly preparing to discuss a mysterious third customs model for post-Brexit trade with the Cabinet in a bid to overcome disagreement on the issue.
Chancellor Philip Hammond, viewed as one of the Cabinet ministers favouring a soft Brexit, told the Commons: "We have to listen to what business is telling us and make sure that we deliver a Brexit which delivers the needs of business". Health secretary Jeremy Hunt responded by calling Airbus's warning "completely inappropriate", while Boris Johnson, the Brexit-supporting foreign secretary, was cited in the United Kingdom media as saying "f*** business".
His intervention will be seen as a shot across the bows to senior ministers, such as Foreign Secretary Boris Johnson, who have reportedly been considering resigning if Theresa May gives too much ground to those pressing to keep Britain as close to the European Union as possible after Brexit, potentially triggering a leadership contest.
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Earlier, Portugal coach Fernando Santos said he hoped Ronaldo would remain part of the global set-up. Obviously I'm very happy for (Cavani's) goals and that they helped us win.
Cabinet tensions are high ahead of the Chequers gathering, with the potential for Brexiteer ministers such as Mr Johnson to quit unless they get their way.
The British Chambers of Commerce (BCC) has published the two-dozen top real-world questions being asked on Brexit by businesses across the United Kingdom - and says the government has managed to make limited progress on just 2 of the 23 issues where clarity is urgently needed so that firms can plan their trade following the UK's departure from the EU.
"The sooner we get a precise United Kingdom proposal on the Irish border, the better the chance to finalise the Brexit negotiations this year", he said.
He hoped the white paper would bring "the necessary clarity, realism and impetus to these negotiations".
JioGigaFiber to JioPhone 2: Top 10 announcements from the Reliance AGM 2018
This is a record that no technology company has been able to achieve anywhere in the world, he added. Jio is determined to move India to be the leader in fixed line broadband in the country.