May is trying to bolster her authority ahead of a crucial new phase in Brexit negotiations on Britain’s divorce from the European Union.
As Parliament returned Monday from its Christmas break, May was summoning ministers to 10 Downing St. to be moved, promoted or demoted.
Several senior ministers are expected to stay, including Foreign Secretary Boris Johnson and Brexit Secretary David Davis.
In the first announcement, Northern Ireland Secretary James Brokenshire says he is resigning due to health reasons.
His resignation comes amid a continuing political crisis in Northern Ireland, whose power-sharing administration has been suspended for a year amid a stalemate between the main Irish nationalist and British unionist parties.