Boris Johnson “must rest up” after he was moved from intensive care with coronavirus, his father has said.
“He almost took one for the team and we’ve got to make sure we play properly now,” Stanley Johnson said.
Scientific adviser Prof Neil Ferguson, who was asked about coming out of lockdown, said it would likely “be targeted by age, by geography”.
Meanwhile, the government has launched a campaign urging people to stay at home over the Easter Bank Holiday.
Downing Street said the prime minister was in “very good spirits” after being discharged from intensive care at St Thomas’ Hospital in London on Thursday evening.
“The prime minister is back on a ward and continuing his recovery which is at an early stage,” his spokesman said.
Earlier, Stanley Johnson spoke of his “relief” that the prime minister had begun his recovery, adding that he thought his illness had “got the whole country to realize this is a serious event”.
He said that there would have to be a “period of adjustment” before the PM returned to work in Downing Street.
Prof Ferguson, of Imperial College London, told Today that work to end the coronavirus lockdown in the UK was the “number one topic and priority” both in the scientific community and in government. “Every waking minute, as it were,” he said.
Speaking about what measures might be needed to end the lockdown, Prof Ferguson said the UK would have to introduce larger levels of testing at a community level “to isolate cases more effectively”.
However, he suggested the lockdown would have to remain in place for “several more weeks”.
It comes as Housing Secretary Robert Jenrick defended his travel moves amid reports he flouted lockdown rules.
The MP for Newark in Nottinghamshire is said to have travelled from London to a second home in Herefordshire, and separately visited his parents in neighbouring Shropshire, according to the Daily Mail and the Guardian.
The government has advised against travel to second homes – and urged people to distance themselves from elderly relatives.
Mr Jenrick said he had been in London on ministerial duties and left for what he said was a family home in Herefordshire to join his wife and children.
He added that he visited his parents to deliver essentials, including medicines – allowed by the rules.
Downing Street has defended Mr Jenrick, saying it was “not an unnecessary journey” for cabinet ministers commuting to and from London to rejoin their family.
“We’re confident that he complied with the social distancing rules,” a spokesman said.
Shadow home secretary Nick Thomas-Symonds said it was “important for public confidence” that Mr Jenrick explained the purpose of the journey.
But he added that if the housing secretary had delivered medicine to his parents, “clearly… it fits within the four exceptions”.
Prof Paul Cosford, medical director for Public Health England, said government guidelines were “quite clear” that people must stay at home except in one of four circumstances, including exercise, essential shopping for food and medicines, healthcare and essential work.
“I can’t comment on Mr Jenrick, it sounds as if what he did was within one of the four guidelines to me, but others will obviously have to think about that more,” he told the Today programme.
Asked about the government’s lockdown exit strategy, Prof Cosford said he “could conceive of circumstances in which some of the restrictions are lifted sooner and some are lifted later”, but cautioned that there was still an “awfully long way to go”.
Meanwhile, the German army is donating 60 mobile ventilators to the NHS. There are currently 10,000 available in the UK and the government says 18,000 are needed.
Thousands of masks and personal protective equipment (PPE) suits for the UK are also scheduled to arrive at RAF Brize Norton later on Friday from Nato ally Turkey.
The number of people to have died in hospital in the UK after testing positive for coronavirus has risen to 7,978, officials announced on Thursday – up 881 on the previous day.