Health Secretary Matt Hancock delivered the briefing from Downing Street on his own. It’s the first time a standard daily briefing has not had an expert present.
The latest figures from the Department of Health show that a total of 40,261 people have died in hospitals, care homes and the wider community after testing positive for coronavirus in the UK as of 5pm on Thursday – a rise of 357 on the previous count.
As of 9am 5 June, there have been 5,214,277 Covid-19 tests, with 207,231 tests on 4 June. Of those, 283,311 people have tested positive.
Mr Hancock said the severe death toll will make him "redouble" his determination to deal with coronavirus.
The Health Secretary told the Downing Street briefing: "I think the day that the number of deaths from coronavirus has gone over 40,000 is a time of sorrow for us all.
"We've got to remember that each one of these is an impact on a family that will never be the same again and my heart goes out to them all.
"And it makes me redouble my determination to deal with this virus and to get that incidence right down and the way you get the incidence down is... to keep the R below one."
Face coverings to be mandatory in hospitals from June 15
Hospital visitors and outpatients will need to wear face coverings and all hospital staff will be required to wear surgical masks in England from June 15, Health Secretary Matt Hancock has announced.
He told the daily Downing Street press conference: "As the NHS reopens right across the country, it's critically important to stop the spread amongst staff, patients and visitors too.
"So today we're setting out that all hospital visitors and outpatients will need to wear face coverings.
"One of the things that we've learnt is that those in hospital, those who are working in hospital, are more likely to catch coronavirus whether they work in a clinical setting or not.
"And so to offer even greater protection we're also providing new guidance for NHS staff in England which will come into force again on June 15 and all hospital staff will be required to wear type one or two surgical masks.
"And this will cover all staff working in hospital, it will apply at all times - not just when they are doing life-saving work on the frontline - and it will apply in all areas, except those areas designated as Covid-secure workplaces."
Local lockdowns could be implemented
Matt Hancock said Sage believes the R is below one and said local lockdowns would be used when flare-ups are spotted, pointing towards a success in Weston-super-Mare.
The Health Secretary told the Downing Street briefing: "The discussion of the higher R in the north-west and the south-west that's estimated compared to the rest of the country is an important part of moving towards a more localised approach rather than a national approach to the lockdown.
“The overall view of Sage is that the R is between 0.7 and 0.9 and it is higher in the south-west of England and the north-west but it remains below 1 in each area.
"That doesn't take away from the need that we spot and crack down on localised outbreaks.
"We want to increasingly have an approach in tackling local lockdowns where we spot a flare-up.
"We've been doing this over the last few weeks, for instance there was a flare-up in Weston-super-Mare which we successfully got under control."
People who have recovered from coronavirus encouraged to donate blood plasma
Mr Hancock encouraged people who had recovered from coronavirus to donate their blood plasma - as he revealed he had made a donation.
He said: "If you have had the virus, then you can help make a difference. Because by donating your plasma from your blood that has your antibodies in it, then you can help somebody who is currently suffering in hospital with coronavirus.
"I did this earlier today, I gave my antibodies, and the process is simple, it's straightforward.
"If you have had coronavirus, if you go to the NHS blood and transplant website... then you too can donate your antibodies and help protect somebody who is currently in hospital with coronavirus.
"And I'd encourage anybody who can do that to step forward."
People urged not to take part in protests
The Health Secretary urged people not to take part in mass demonstrations over the weekend in breach of lockdown rules.
The Health Secretary told the No 10 briefing: "Like so many I am appalled by the death of George Floyd and I understand why people are deeply upset but we are still facing a health crisis and coronavirus remains a real threat.
"The reason that it is vital that people stick to the rules this weekend is to protect themselves and their family from this horrific disease.
"So please for the safety of your loved ones do not attend large gatherings including demonstrations of more than six people."