"The reshuffle was a farce showing the prime minister is weak".
The EU and the United Kingdom entered the second phase of the negotiation process.
It is not envisaged to be satisfied with replacing resigned, as it did in cases of Fallon and Patel, but it is not likely that changes will affect main figures of government, such as Philip Hammond, Chancellor of Exchequer; Boris Johnson, head of Foreign Office; Amber Rudd, Interior proprietor, or David Davis, Minister of Brexit.
Greening had tried to refuse to switch jobs once before, when former Prime Minister David Cameron moved her from transport to global development, according to an official familiar with past reshuffles.
The reshuffle was sparked in part by the resignation of May's ally, Damian Green as the de-facto deputy prime minister, after police who were investigating a separate matter revealed they had found thousands of pornographic images on his computer.
Theresa May's new ministerial team is more diverse and will "better reflect the country which it serves", Downing Street said.
"Damian Green's departure before Christmas means that some changes do have to be made, and I will be making some changes", Mr. "It will be soon".
Despite winning agreement from the European Union to move Brexit talks to a discussion of future trade and a transitional deal, May has been criticised at home for her approach to healthcare, housing, transport and Britain's departure from the bloc.
Mrs May's Cabinet met for the first time since a misfired reshuffle of top jobs on Monday, which saw Justine Greening walk out as education secretary rather than accept a move to work and pensions, while Jeremy Hunt turned down the PM's offer of the business brief, insisting instead on an expanded health and social care role.
Labour's shadow health secretary Jonathan Ashworth was scornful of the prospect of Hunt as deputy prime minister.
Sir Patrick McLoughlin: The Tory Chairman is vulnerable after overseeing the party's election machine during last year's disastrous campaign.
Justice Minister Dominic Raab, an ardent Brexit supporter, is reported to be in line for a top job, while Ms.
Lewis had until today been the Minister of State for Immigration and was the first minister to have been summoned to No.10 to meet with the Prime Minister this morning.
May has said she intends to stay in office "as long as people want me to serve", but a year ago saw numerous reports of plots to oust her - and many ministers will have their eye on a future leadership challenge.
"I'm not a quitter".
But pressed on the BBC1's Andrew Marr Show on whether she would still be there the next time the country goes to the polls, she replied: "Obviously I serve as long as people want me to serve".
But aides had long said Monday's moves were less important that those on Tuesday, when May promoted lawmakers to junior positions in preparation of a wider reshuffle after Brexit.