Pubs may be forced to close in areas under local coronavirus lockdowns so that schools can remain open, Downing Street has said.
Boris Johnson has said the UK has a moral responsibility to get children back into the classroom.
Meanwhile, Nicola Sturgeon has apologised to Scottish exam students who were marked down "because of an algorithm".
She said: "In a very difficult and unprecedented situation, we took decisions that we thought on balance were the right ones."
The number of NHS contact tracers are to be slashed by a third, while the rest are set to be redeployed locally.
Announcing the changes to the NHS Test and Trace programme, the Department for Health and Social Care said it would cut the number of national contact tracers by 6,000 by 24 August.
Risk to children low, study to suggest
One of the most detailed studies yet will show that it is safe for schools to fully reopen next month, a leading child health expert has assured parents and students, writes Rob Merrick.
Professor Russell Viner, president of the Royal College of Paediatrics and Child Health, said that the research, which was carried out in 100 institutions in the UK, will confirm “there is very little evidence” of coronavirus transmission where pupils have returned.
“The risks to children from Covid are very low and the risks of school closures we know are very serious,” he said.
'Very low' risks to children mean school reopenings are safe, expert says
The IndependentPublic Health England research finds ‘very little evidence’ of coronavirus transmission where pupils have returnedWeight of evidence suggesting school re-opening can be safe
Professor Russell Viner, president of the Royal College of Paediatrics and Child Health and a member of Sage, has taken to the airwaves to hammer home his message that studies suggest children are"very minor players in the transmission overall" of coronavirus.
The children's doctor spoke out overnight to say research would prove re-opening Britain's schools would be safe.
On Monday morning he told BBC Radio 4's Today programme: "There are five studies from around the world from New South Wales, from Australia, Singapore, from Ireland, from Germany, and from France, and in each of those there appears to be very, very little transmission in schools.
"We know that children can and do transmit this virus, of course they do, but they're very minor players in the transmission overall, particularly younger children.
"It's increasingly clear that older children - teenagers probably - transmit as much as adults, but schools themselves play very little role.
"They're a closed setting but actually we see very few outbreaks in schools, large outbreaks, and actually there's very little transmission from child to child or child to adult, actually much of the transmission in schools is from adults bringing it in, particularly staff.
"There's increasing evidence in the UK and the government is doing a number of studies which have showed apparently very little transmission and very little infection when schools were open in England."
Daily cases rise above 1,000
The UK’s daily number of new coronavirus cases has topped 1,000 for the first time in more than a month, writes Zoe Tidman.
The government reported 1,062 more people had tested positive for Covid-19 in the 24-hour period leading up to Sunday morning.
This is the largest daily increase since late June.
Red Cross sends aid to North Korea
The Red Cross has sent more than 43,000 volunteers to North Korea to help fight Covid-19, an it said on Monday.
North Korean leader Kim Jong-un declared an emergency last month and imposed a lockdown on Kaesong, near the border with South Korea, after a man who defected in 2017 returned to the city showing coronavirus symptoms.
Heavy rain and flooding in recent days have also sparked concern about crop damage and food supplies in the isolated country.
Red Cross volunteers will also provide flood relief.
Burnham calls for better testing before schools reopen
Andy Burnham has added his voice to the chorus calling for improvements to the UK's testing regime as a prerequisite for the full reopening of schools.
Greater Manchester's mayor has said that getting children back into classrooms should be a top priority.
However, he told BBC Breakfast on Monday that the test and trace programme had to be better to give parents the confidence to send their children back to school.
He added: "It's got to be the top priority, getting kids back to school, because they have had huge disruption this year.
"We have got to make every arrangement possible so that people can have that peace of mind.
"But it does point then at the test and trace system, it isn't yet good enough and I am saying to the government we need to work together to get this system right over August so that we can then both of us give that confidence to those parents."
Surgeons told not to discuss PPE shortages
Dozens of surgeons have reported being told by the NHS employer to stop discussing shortages of personal protective equipment (PPE) during the coronavirus crisis, writes Shaun Lintern.
The Confederation of British Surgery (CBS) said almost 70 surgeons working in major hospitals around the country had been warned off discussing a lack of PPE by their trust.
A third of surgeons said the supply of PPE was inadequate at their hospital, with many complaining of inconsistent guidance, rationing of supplies and poor quality PPE when it was available.
Australia sees deadliest day, and borders to stay shut
Australia's internal borders are unlikely to reopen before Christmas, Scott Morrison has said.
It came as daily infections in the Melbourne hotspot appeared to slow - but 19 deaths were recorded there, Australia's highest one-day toll even without counting the rest of the country.
Australia's federal political system has led to its eight states and territories taking different measures in response to the crisis, resulting in several internal border closures.
Mr Morrison said he believed Melbourne's strict lockdown was working.
"I am more hopeful of that today than I was in the course of the past week," he told reporters in Canberra, as he called on state leaders to cooperate to allow stranded residents to return home.
Strip Serco of test-and-trace contract, Labour says
A new lucrative contract for private giant Serco to run test-and-trace services should be stopped, Labour says – arguing the stakes are too high to “tolerate failure”, writes Rob Merrick.
The government is urged not to shell out a further £300m in a decision due later this month, amid rising criticism of the company’s failure to find and isolate coronavirus cases.
Instead, the system should be led by local public health leaders, who have proved they are more successful in tracing the contacts of infected people, Labour said.
Schools to get test kits
Helen Whately has said it is a "national priority" to get children back to school in autumn.
The care minister told Sky News: "Getting our children back to school this autumn is absolutely a national priority, we're determined to see children back to school.
"I know that teachers and parents have made huge efforts to continue children's education from home.
"But it's not the same as children being in school and sadly we have seen children from disadvantaged backgrounds more likely to fall behind during this time, so it's essential that we have children back at school this autumn."
She added: "Schools will be a safe environment for children to be taught in, of course in the event a child has a temperature or any type of symptoms, it's very important they get a rapid test.
"Schools will be provided with home test kits."
Russia figures
Russia reported 5,118 new cases of coronavirus on Monday, pushing the country's tally to 892,654 - the fourth largest in the world after the US, Brazil and India.
The official death toll rose to 15,001 after 70 people died in the last 24 hours.
California public health director resigns
The head of California's public health department has resigned.
Dr Sonia Angell announced her departure late on Sunday, just days after the state announced a fix for a glitch that caused a lag in collecting coronavirus test information used to make decisions about reopening businesses and schools.
Dr Angell said she was departing from her role as director and state public health officer at the California Department of Public Health in a letter to staff released by the California Health and Human Services Agency.
She did not give a specific reason.
Further lockdown easing in Wales
Gyms, swimming pools, leisure centres and indoor fitness studios are reopening in Wales.
Unlike the rest of the UK, children's indoor play areas can also open, though places like ball pits, which cannot be easily cleaned, will remain closed.
The Welsh government has boosted the powers of councils to enforce laws designed to prevent the spread of Covid-19 in newly reopened businesses.
The latest changes to coronavirus regulations in Wales have come into force one week after pubs and restaurants in the country were able to open indoors for the first time since lockdown began in March.
The Welsh government said it was "continuing to explore" whether people can be allowed to meet indoors others who are not already part of their extended household from 15 August.
Schools could stay closed during local outbreaks, Drakeford warns
Mark Drakeford has said some schools could close in the event of a local coronavirus outbreak.
The Welsh first minister told BBC Breakfast: "Every local flare-up is different. In some places not reopening schools would be part of a plan, in other sorts of outbreaks that may not be necessary.
"It's down to the local circumstances, down to the team on the ground. and they will then advise Welsh ministers."
Mr Drakeford added: "There are a series of options that we could draw on if we needed to. Our top plan is to get every child back in school in September so that they are learning - these children have been deprived of their learning for months."
Pub customer told to self-isolate
Customers of a pub in the West Midlands have been told to immediately self-isolate after an outbreak of coronavirus emerged following a barbecue there, writes Jane Dalton.
About 70 people were at the event at the Soho Foundry Tavern in Smethwick last Sunday, and three – including some staff – have since tested positive for Covid-19, council officials say.
The pub closed voluntarily on Thursday after the cases became known.
US would share vaccine if it developed one - after we're finished with it, Azar says
Any vaccine or treatment for Covid-19 would be shared fairly with the rest of the world, but only once Americans' needs have been satisfied, Alex Azar has said.
Donald Trump's health secretary said that "of course" Washington's first priority was to develop treatements for us in the US.
He added in comments on Monday: "But we anticipate having capacity that, once those needs are satisfied, those products would be available in the world community according to fair and equitable distributions that we would consult in the international community on."
He did not elaborate.
There are more than 200 COVID-19 vaccine candidates in development around the world, including more than 20 in human clinical trials.
Mr Trump has vowed to have a shot ready before year's end, though they typically take several years to develop and test for safety and effectiveness.
Hong Kong update
Hong Kong reported 69 new coronavirus cases on Monday, of which 67 were locally transmitted.
City authorities are trying to contain a resurgence of the virus over the last six weeks.
Since late January, more than 4,000 people have been infected in Hong Kong, 55 of whom have died.
On Sunday, Hong Kong reported 72 new cases.
Report says ministers should fund changes to unhealthy recipes
Food manufacturers should be given taxpayer help to research how to re-formulate unhealthy foods to help tackle Britain’s obesity crisis, a new report has said, writes Shaun Lintern.
The non-profit think tank Demos also said ministers must consider subsidising healthy foods to help tackle food market flaws, which it says leave 20 million people unable to afford healthy food.
The government unveiled a new obesity strategy last month as evidence shows those who are overweight have a greater risk of becoming severely ill or dying from coronavirus.
Indonesia figures
Indonesia reported 1,687 new coronavirus cases on Monday, bringing its total to 127,083, government data showed.
The southeast Asian country also added 42 new deaths, taking the overall toll to 5,765.
Manchester Crown Court forced to close
Manchester Crown Court has closed for a second time after three people tested positive for Covid-19, the Manchester Evening News reports.
The closure on Monday morning followed positive tests in two people.
Last week the court closed for half a day for a deep clean following one positive test, the paper reported.
Clearing could be busiest yet after gap year plans ruined by virus
There could be a record number of students trying to secure a place a university through clearing, the head of the admissions service has predicted, writes Tim Wyatt.
Although A-Level results are less than a week away, almost three-quarters of Britain’s leading universities have vacancies for undergraduate courses on the Universities and Colleges Admissions Service (UCAS) website.
Clare Marchant, the chief executive of UCAS, said she thought as many as 80,000 applicants could find a place at university through clearing, up from 73,000 last year.
