She, however, underlined she did not want her government to be "defined by Brexit" as work gets underway for Britain to begin its exit from the European Union following the historic June 23 referendum.
"It will be the responsibility of everyone sitting around the Cabinet table to make Brexit work for Britain," she said.
"We will not allow the country to be defined by Brexit, but instead will build the education, skills and social mobility to allow everyone to prosper from the opportunities of leaving the EU," she added.
Of the 22 full members of the Cabinet and five who have the right to attend Cabinet meetings, only five - Health Secretary Jeremy Hunt, Defence Secretary Michael Fallon, Welsh Secretary Alun Cairns, Scottish Secretary David Mundell and Attorney General Jeremy Wright - retained the roles they held previously under David Cameron.
Indian-origin minister Priti Patel, who previously had the right to attend Cabinet meetings as a junior minister, today took her position as a full-fledged minister in charge of the Department for International Development (DfID).
David Davis has been put in charge of a brand new ministry to take the UK out of the EU.
May, who has already held talks with Scottish First Minister Nicola Sturgeon and Welsh First Minister Carwyn Jones, received a boost yesterday when MPs overwhelmingly voted by a majority of 355 to proceed with the full renewal of the UK's Trident nuclear weapons system.
Shefaces her first Prime Minister's Questions tomorrow, after which she will travel to Germany for talks with German Chancellor Angela Merkel.
May has said she does not expect the UK to officially notify the EU of its intention to leave, which involves triggering Article 50 of the Lisbon Treaty, before the end of the year.
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