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 supported by science.
The next step could see some hospitality businesses and other public places reopen – “if the numbers support it” – but not earlier than 1 July.
He said these steps formed part of a “first sketch of a roadmap for reopening society”.
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.”
Mr Johnson also confirmed that fines for the “for the small minority who break” lockdown rules will increase.
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.”
The PM explained how the “R” number – the reproduction rate of the virus – would be crucial in deciding whether lockdown could be eased further.
Experts have said that keeping R below 1 – meaning one person with the virus passes it on to one other person – is the priority.
“It depends on all of us – the entire country – to follow the advice, to observe social distancing, and to keep that R down,” he said.
The PM 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”, he added.
He said in addition to being able to leave home as many times as they wish for exercise or to sunbathe in parks, people in England would also be able to drive to other destinations.
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.
In a joint statement later, Mr Johnson and French President Emmanuel Macron agreed quarantine measures would not apply between France and the UK “at this stage”.