The Queen and other senior royals sent messages to Mr Johnson's family and his pregnant fiancee, Carrie Symonds, saying they were thinking of them, and wished the PM a full and speedy recovery.
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Latest on lockdown
A ban on public gatherings of more than two people and the closure of shops selling non-essential goods were among the series of restrictions announced by Mr Johnson on 23 March to tackle the spread of coronavirus.
He had said a relaxation of the rules would be considered in three weeks, which would be 13 April.
But on Tuesday, Downing Street suggested that the review would not go ahead on the scheduled date and would instead take place after the three-week mark.
Mr Argar told BBC Breakfast on Wednesday: "We need to start seeing the numbers coming down and that's when you're in the negative.
"That's when you have a sense when that's sustained over a period of time, that you can see it coming out of that. We're not there yet and I don't exactly know when we will be."
He urged people to stay at home "however lovely the weather this Easter weekend".
"If we are, as the statistics appear to show, making a little bit of progress, now's the time to hold to it," he said.
Also at Tuesday's briefing, Mr Raab was also asked about whether his role deputising for Mr Johnson gave him full prime ministerial responsibility.
The foreign secretary said he was standing in for the prime minister "whenever necessary" - including leading the daily meetings of the coronavirus "war cabinet".
Mr Raab said decisions would be made by "collective cabinet responsibility - so that is the same as before".
"But we've got very clear directions, very clear instructions from the prime minister, and we're focused with total unity and total resolve on implementing them so that when he's back, I hope in very short order, we will have made the progress that he would expect and that the country would expect," Mr Raab added.
Meanwhile, the first patients have been admitted to the NHS Nightingale Hospital in east London - a temporary facility set up at the ExCel conference centre.
The admissions come two weeks after the hospital with a planned capacity of 4,000 was formally announced - although an NHS spokesperson stressed limits had not been reached at other sites in London.
It came as the number of coronavirus hospital deaths in the UK rose to 6,159 on Tuesday - a record increase of 786 in a day, the Department of Health and Social Care said, compared with 439 on Monday.
However, the government's chief scientific adviser told the Downing Street briefing the number of coronavirus cases in the UK "could be moving in the right direction".
Sir Patrick Vallance said it was "possible that we're beginning to see... the curve flattening".
As of 09:00 BST on Tuesday, 213,181 people have been tested, of which 55,242 tested positive, the Department of Health and Social Care said.
Overall, 266,694 tests have been concluded, with 14,006 tests carried out on Monday.
In other developments:
- In London 14 public transport staff have died from the virus, including nine bus workers. He said some buses were trialling allowing passengers to get on the bus only through the back doors to avoid going near the driver
- Supermarket Tesco said most food would still need to be bought in store as it was not able to meet home delivery demand, while Sainsbury's said it was removing restrictions on thousands of products as stock levels recover
- A doctor who specialised in treating the elderly has died at a London hospital after testing positive for Covid-19
- Vets have said cat owners should keep their pets indoors to help stop the spread of the virus
- Most of the public support police measures like fines and roadblocks to tackle the coronavirus, a YouGov survey suggests, but a third of those questioned thought forces in Britain had gone too far in some cases
- The months-long lockdown in the city of Wuhan in China's Hubei province - where the coronavirus pandemic started - has been lifted
- The number of people in France who have died from the coronavirus has now risen above 10,000.
- The US recorded the most coronavirus deaths in a single day with 1,736 fatalities reported on Tuesday. Country music singer-songwriter John Prine was among those to have died
BBC
