The state will be "under the microscope", Boris Johnson says, as Labour urges an earlier start date.
Pregnant women will be directed to centres offering Pfizer and Moderna vaccines when booking.
The 75-year-old was convicted in 2016 of genocide during the conflict in the former Yugoslavia.
On Tuesday, an inquest found that 10 people shot in west Belfast in 1971 were innocent.
Nine-year-old Jordan Banks was "the brightest star" and "our everything", his family says.