Prime Minister Boris Johnson says reopening schools next month is a "national priority".
Mr Johnson wrote in a newspaper article that there is a "moral duty" to get all pupils back to school in September, raising the prospect of "trade-offs" in the coronavirus lockdown.
Some scientists have suggested that pubs or shops may have to close again to allow all pupils to return to classes in just a few weeks.
Mr Johnson wrote in the Mail on Sunday: "Keeping our schools closed a moment longer than absolutely necessary is socially intolerable, economically unsustainable and morally indefensible."
He suggests that schools should be the last to close, meaning that businesses could be forced to shut in the event of any further local lockdowns.
Meanwhile, a further 55 deaths of Covid-19 patients were announced on Saturday, bringing the UK death toll to 46,566 in hospitals, care homes and the wider community.
There were 758 new cases found in the 24 hours to 9am on Saturday. One of those was in Hull, where 1,578 people have so far tested positive - giving it an infection rate of 607.4 cases per 100,000 people. The average infection rate in England is 474.9.
None were recorded in the East Riding where there has been 1,658 positive tests and an infection rate of 486.
There were no deaths recorded in East Yorkshire on Saturday.
New rules also came into force on Saturday, which say face coverings must be worn in all indoor settings where people are likely to come into contact with others they do not know. Face masks have been mandatory in shops since last month. Click here for the full list of places where masks must be worn.
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