Boris Johnson delivered an address outlining how lockdown measures, which have been established since Monday 23 March, are to ease across England.
Plans have also been put in place for schools to reopen in the coming weeks, as long as the spread of Covid-19 remains "on the downward slope".
However, schools in other parts of the UK in Scotland, Wales and Northern Ireland are not expected to open at the same time as those in England.
In an update published by the government on Monday 11 May, it states that by Monday 1 June "at the earliest", primary schools in England "may be able to welcome back children in key transition years".
"Secondary schools, sixth forms and colleges will also work towards the possibility of providing some face-to-face contact with young people in Year 10 and Year 12 to help them prepare for exams next year," the Department for Education states.
However, "progress will be monitored every day" and will determine whether it is safe to reopen schools for an increased number of pupils.
"If the virus stays on the downward slope, and the R remains below 1, then - and only then - will it become safe to go further, move to the second step and reopen schools," the government outlines.
The government adds that its aim is "for all primary school children to return to school before the summer for a month if feasible, though this will be kept under review".
"The Department of Education will engage closely with schools and early years providers to develop further detail and guidance on how schools should facilitate this."