Boris Johnson has unveiled a “conditional plan” to reopen society, allowing people in England to spend more time outdoors from Wednesday.
The PM also said people who could not work from home should return to the workplace – but avoid public transport.
He said a new Covid Alert System with five levels would govern how quickly lockdown restrictions could be eased.
He hoped the next step “at the earliest by 1 June” would be for some primary pupils to return to school in England.
In an address to the nation, Mr Johnson said this stage would also involve reopening shops – but he cautioned this would only happen if the science supported it.
The next step could see some hospitality businesses and other public places reopen – “if the numbers support it” – but not earlier than 1 July.
The PM added: “This is not the time simply to end the lockdown this week.
“Instead we are taking the first careful steps to modify our measures.”
Clarifying the conditions in which schools and shops would reopen, Mr Johnson said: “Throughout this period of the next two months we will be driven not by mere hope or economic necessity.
“We are going to be driven by the science, the data and public health.
“And I must stress again all of this is conditional, it all depends on a series of big ifs.”
He said those who could not work from home would now be encouraged to return to work – but they should avoid using public transport to get there if possible.
Mr Johnson mentioned construction and manufacturing as examples of the sorts of industries where restarting would now be explicitly encouraged.
Workplaces would receive guidance on how to become “Covid secure”, Mr Johnson added.
The PM also said he was “serving notice” that it would soon be the time to impose a quarantine on people coming into the country by air.
Labour leader Sir Keir Starmer said Mr Johnson’s speech lacked “clarity and consensus” and raised “as many questions as it answers”.
“What the country wanted tonight was clarity and consensus, and I’m afraid we’ve got neither,” the Labour leader said.
“This statement raises as many questions as it answers, and we see the prospect of England, Scotland and Wales, pulling in different directions. It’s big gap here for the government to make up.”
Mr Johnson’s speech came hours after Scottish First Minister Nicola Sturgeon said she felt ending the previous “stay at home” message was the wrong choice for Scotland.
The PM earlier unveiled the new message of “stay alert, control the virus, save lives” in England – but Ms Sturgeon said it would not apply in Scotland at the moment.
Wales’ health minister Vaughan Gething also said there had not been a “four-nations agreement” on the new message and that the advice to “stay at home” in Wales was unchanged.
Scotland, Wales and Northern Ireland have powers over their own lockdown restrictions, with England’s measures set by the government at Westminster and leaders have expressed a wish to move forward as one – though they may do so at different speeds.
Mr Johnson said in his speech he had consulted “across the political spectrum, across all four nations of the UK” and that his plan was a “a general consensus on what we could do”.
A further 269 people have died in the UK after testing positive for coronavirus, taking the total number of deaths recorded to 31,855.
The number of deaths recorded tends to be lower over the weekend because of reporting delays.
The government has also missed its target of 100,000 coronavirus tests a day for the eighth day in a row, with 92,837 tests on Saturday.
In other developments:
- A further 178 deaths of people with coronavirus have been reported by NHS England
- There were also 12 more deaths reported in Wales, 10 in Scotland and five in Northern Ireland
- The government missed its target of 100,000 tests a day for the eighth day in a row, with 92,837 tests on Saturday
- The Department of Health has confirmed 50,000 coronavirus test samples were sent to the US earlier this week after problems in UK laboratories
- Mr Jenrick said a contact-tracing app being trialled on the Isle of Wight had been downloaded by about 50,000 people. Asked about reports a second app was being developed, he said the government was “learning lessons” from apps used by other countries
- More than 70 public figures – including Baroness Doreen Lawrence and author Malorie Blackman – are calling for a full independent public inquiry into deaths from Covid-19 among people from ethnic minority backgrounds
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