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.
But the reorganization quickly became more remarkable for what May didn't do rather than what she did, highlighting the difficulties imposed by Brexit and the erosion of the prime minister's authority since the ill-judged vote in June that cost her party its parliamentary majority.
The Conservatives' official media account tweeted its congratulations to Brexiteer Chris Grayling as the Tory party's new chair - but staff rapidly had to backtrack and delete the message.
The analysts say this is an attempt of the government to demonstrate to the European Union that the country has serious intentions to leave the community, even if it fails to reach a trade agreement with other countries.
Theresa May's new ministerial team is more diverse and will "better reflect the country which it serves", Downing Street said.
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The biggest casualty was the education secretary Justine Greening, who after spending nearly three hours at Number 10 quit the government, rather than take on the Work and Pensions portfolio.
Speculation remained rife at Westminster that several big names were on their way out of the Cabinet, with Education Secretary Justine Greening and the Leader of the Commons Andrea Leadsom reported to be vulnerable as the Prime Minister sought to assert her authority.
Farage asked for the meeting after Barnier met with anti-Brexit British politicians previous year, including Andrew Adonis, from the opposition Labour party, who had advised May on Brexit until he resigned from his post in December in protest at her appeasement of hard eurosceptics.
The reshuffle, which will continue into tomorrow, is being seen as an opportunity for May to promote more women, with female ministers only now making up six of the 23 full members of her top team.
Ms May was reportedly set to create a new "no-deal" cabinet post on Monday with a responsibility to prepare for a possible breakdown in the talks.
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The cabinet reshuffle is being viewed as a chance at a fresh start, although it also brings risks of upsetting the delicate balance of eurosceptic and pro-European ministers.
After starting the two-year Brexit process in March last year, Britain struck a deal in December on the financial settlement with Brussels, as well as expatriate rights and the Irish border.
Meanwhile Dominic Raab, justice minister and an ardent Brexit supporter, is tipped to be in line for a top job.
Brexit secretary David Davis wrote to Theresa May last month claiming that the EU's plans could jeopardise contracts and force firms to relocate to the continent, according to the FT.
"It allows a new generation of gifted ministers to step up and make life better for people across the whole United Kingdom", she said in a statement.
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Her shuffle was complicated by the resignation of the United Kingdom's minister for Northern Ireland amid a long-running political crisis in Belfast. He was replaced by the culture secretary, Karen Bradley, who will take on the hard task of attempting to resolve the impasse in the province between the Democratic Unionists and Sinn Fein which has seen no administration there for a year.