Justice secretary Michael Gove, health secretary Jeremy Hunt, education secretary Nicky Morgan, culture secretary John Whittingdale and chancellor of the Duchy of Lancaster Oliver Letwin all lost their jobs as part of the reshuffle.
Gove, who challenged May for the leadership of the centre-right Conservative party, was criticised by some for appearing to scupper former London mayor and now Foreign Secretary Boris Johnson's chances of taking the helm by launching his own bid.
Mr Gove becomes the second major casualty from David Cameron's cabinet, joining former Chancellor George Osborne on the backbenches.
In her first speech as Prime Minister on Wednesday, Mrs May vowed to "fight against burning injustice" in Britain and build "a country that works for everyone".
While Osborne's exit came as less of a surprise, being a close Cameron aide, Johnson's appointment as foreign secretary was more unexpected.
Speaking ahead of the visit, the Prime Minister said: "I believe with all my heart in the United Kingdom - the precious bond between England, Scotland, Wales and Northern Ireland".
Also mindful of loading her Government with the privately educated and privileged, Justine Greening, who was educated at a local comprehensive school, was told to pack up her things at the Department for International Development and unpack them as the new Education Secretary.
The vote to quit the European Union has had a chilling effect on the British economy but there will be no emergency budget, Chancellor Philip Hammond has said.
As the shockwaves from her radical Cabinet clear-out continued to surge through the Tory party, Mrs May turned her attention to preserving the union as she headed to Edinburgh for talks with SNP First Minister Nicola Sturgeon.
The pro-Brexit MP praised Mrs May's candidacy, so the new prime minister may want to return the compliment, said the Telegraph.
"The test now is to demonstrate that all members of the Tory Government are wholly committed to the priorities Theresa May set out yesterday".
The French foreign minister, Jean-Marc Ayrault, speaking Thursday on Europe 1 radio, said he was "not at all worried" about Johnson, but he added, "You know full well what his style is, his method - during the campaign he lied a lot to the British people". She joined parliament in 2010 and was appointed energy and climate change secretary in 2015. Some Tory MPs doubted that her appointment of right-wingers would help Mrs May deliver her pledge to govern from the centre ground and champion struggling working class families.
One of the first appointments is expected to be a secretary of state for the so-called Brexit department.
That put him at odds with Mr Cameron, an enthusiastic backer of gay marriage.