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The Metropolitan Police said on Tuesday (local time) that two men arrested last week had been charged with terrorism offences and would appear in Westminster Magistrates' Court on Wednesday.
The Metropolitan Police said in a statement that the men were arrested by its Counter Terrorism Command on November 28.
It identified them as Naa’imur Zakariyah Rahman, 20, of north London, and Mohammed Aqib Imran, 21, of southeast Birmingham.
Sky News reported, citing sources, that police had foiled a plot to assassinate May. The report said police believed there was a plan to launch an improvised explosive device at Downing St and, in the chaos that ensued, attack and kill May.
Earlier, May's spokesman said Britain had thwarted nine plots in the last 12 months.