Primary schools in England could reopen to some year groups from 1 June “at the earliest”, says Boris Johnson.
The prime minister said a phased return to school would begin with pupils in Reception, Year 1 and Year 6, if infection rates at the time allow it.
For most pupils, schools have been closed by the Covid-19 outbreak since 20 March.
But the National Education Union said the reopening plan was “nothing short of reckless”.
“At the earliest by June 1, after half term, we believe we may be in a position to begin the phased reopening of shops and to get primary pupils back into schools, in stages,” said Mr Johnson.
Secondary schools are likely to stay closed until September.
But the prime minister said there was an “ambition” to get secondary pupils who were facing exams next year – such as Years 10 and 12 – to get some time in school before the summer holidays.
Mr Johnson, announcing the “first careful steps”, said it would be the oldest and some of the youngest in primary school who would go back first – Year 6 who would soon be moving to secondary school and to the Reception class and Year 1.
There were still a “series of big ifs” about the proposals, said the prime minister, and he would “put on the brakes” again if necessary.
But his “roadmap” would mean the beginning of reopening schools in England, which are currently only open to the children of key workers and vulnerable children.
Geoff Barton, leader of the ASCL head teachers’ union, said it was important that the date was not “set in stone”, because it was still not clear “how the reintroduction of such significant numbers of pupils in primary schools can be safely managed”.
He also said the question of protecting equipment for teachers remained unresolved, when social distancing in schools would be “problematic”.
“Unfortunately, we are not persuaded that either of these two simple tests has yet been met,” said Mr Barton.
Mary Bousted, co-leader of the National Education Union, rejected the plan, saying infection rates were too high for it to be safe to bring more pupils into primary schools.
“We must have a national plan for social distancing, hygiene, appropriate PPE and regular testing to ensure our schools and colleges don’t become hot spots for Covid-19,” said Dr Bousted.
In Wales, the First Minister Mark Drakeford has already ruled out following the same timetable for unlocking schools.
“We’re not going to be reopening schools in Wales in the next three weeks, or indeed in June,” he said.
In Scotland, the government has warned that fully reopening primary schools ran the risk of “overwhelming” the NHS.
In Northern Ireland, Education Minister Peter Weir has spoken of a possible phased return of schools in September.