The Government expects pre-school children to be able to return to early years settings, and for Reception, Year 1 and Year 6 pupils to be back in school in "smaller sizes", from the start of next month.
It aims to ensure that the youngest children, and those preparing for secondary school, have "maximum time with their teachers".
The Government's Covid-19 recovery strategy said that the ambition is for all primary school children to return to school before the summer holidays for a month "if feasible" - but this will be kept under review.
The Department of Education will engage with schools and early years providers to develop further detail and guidance on how schools should facilitate this.
The 50-page strategy, published on Monday, added that secondary schools and further education colleges should prepare to begin some "face-to-face contact" with Year 10 and 12 students who have key exams next year.
The plan adds that face coverings should not be used by children under the age of two, or by primary school-age children unassisted.
Schools, colleges and nurseries closed seven weeks ago due to the coronavirus outbreak, remaining open only for vulnerable youngsters and the children of key workers.
The strategy says local authorities and schools should urge more vulnerable children, as well as the children of critical workers, to attend school as there is a "large societal benefit".
The Government is also amending its guidance to clarify that paid childcare, such as nannies and childminders, can take place subject to being able to meet its key public health principles.
The strategy document says this should enable "more working parents to return to work."
Neil Leitch, chief executive of the Early Years Alliance, said that publishing a "vague outline of a strategy" before any detailed guidance is available for childcare providers is "unhelpful" for a sector already under pressure.
He said: "Nurseries, pre-schools and childminders need a clear plan of action on how they are going to be supported, both practically and financially, to reopen as lockdown eases.
"While the road map states that the Government expects children to be able to return to early years settings from June 1 - and for childminders, from as early as this week - the sector urgently needs more detail on exactly how this is expected to work in practice."
Mr Leitch added: "Early years providers are going to face significant changes to the way they operate on a day-to-day basis, including a likely reduction in the demand for childcare places as some parents opt to keep their children home rather than returning to their settings.
"As such, Government urgently needs to outline what steps it is planning to take to ensure that providers are able to remain financially sustainable during this period, as well as how it will ensure that both practitioners and the families they care for can best be kept safe."
One idea being considered by the Scientific Advisory Group for Emergencies (Sage) is if it is safe to change the rules to allow one household to expand and include one other household in the same group.
This could allow two households to share childcare duties, freeing up more people to return to work.
But more than 400,000 people have signed a petition urging the Government to give parents a choice on sending their children back to school if they reopen next month.
And teaching unions have warned that the plan to reopening primary schools by June 1 is "reckless".
Mary Bousted, joint general secretary of the National Education Union (NEU), said the union is advising school leaders that they are in "no position" to start planning for a wider opening yet.
She said: "The National Education Union want schools to move to a wider opening as soon as it is safe to do so, but it is not safe yet. This timetable is reckless."
Headteachers have been "inundated" with questions from their staff and from parents, she said.
"The Government has stoked teachers' anxiety and triggered real confusion because the announcement is inconsistent on the importance of social distancing and how or whether it can be achieved in schools," Dr Bousted added.