Here’s a quick summary of the main stories from the UK:

• People must take lockdown seriously as the UK is "in the eye of a storm" in a situation "much worse than March" says virus expert Professor Peter Horby
• His warning comes as almost 60,000 new cases of coronavirus were reported in the UK on Saturday and the number of deaths after a positive test passed 80,000
• But hope is on the horizon as every adult will be offered a Covid vaccine by the autumn, Health Secretary Matt Hancock says

• Regular rapid testing for people without coronavirus symptoms will start across England this week

• Meanwhile, Home Secretary Priti Patel has said officers "will not hesitate" to enforce lockdown rules as she defended the way police have handled breaches
• In Wales, some councils have not included some jobs like teachers and supermarket staff on their lists of key workers whose children can go to school
• Live-streamed lessons will not be offered to all children in Scotland when the new school terms begins on Monday, according to BBC research

Earlier we heard from Labour leader Sir Keir Starmer, who warned the current lockdown rules "may not be tough enough".

Appearing on BBC One's Andrew Marr Show, he also criticised the government for "mixed messaging" during the pandemic.

Rolling out mass testing and vaccines has been a focus for the scientists and politicians this morning.

More than 1.2 million people in the UK had received a Covid-19 vaccine in the UK as of 3 January, according to the latest government figures, external.

Vaccines are being given to the most vulnerable first, as set out in a list of nine high-priority groups.

The government aims to offer vaccines to everyone in the top four of these priority groups by mid-February - around 13 million people.

Health Secretary Matt Hancock reiterated that time goal this morning - saying 15 February.

This covers all residents in care homes for older adults and their carers, all over-70s, anyone who is clinically extremely vulnerable and frontline health and social care workers

To meet this target, ministers need to deliver more than two million jabs a week by the end of January

Earlier today, Hancock also said everyone over the age of 18 would be offered a coronavirus vaccine by the autumn.

He said the UK was now vaccinating more than 200,000 people a day and around a third of all over-80s had received a jab.

Image source, Getty Images

Live-streamed lessons will not be offered to all children in Scotland when the new school terms begins on Monday, according to BBC research.

Plans for remote learning during the latest lockdown reveal big disparities between Scotland's 32 councils.

Many say live online lessons will be part of a mix of different learning tools offered to pupils but some have ruled it out.

Others have left the decision to individual schools and teachers.

Meanwhile, some vulnerable children and children of key workers who are able to attend school will receive face-to-face teaching in almost normal lessons.

Read more.

Image source, Reuters

Unions have hit back at decisions from some councils in Wales to deny childcare to certain groups of key workers.

The Welsh Government compiled a list of jobs deemed critical, external at the beginning of the Covid pandemic, which was provided to local authorities.

However, some councils compiled their own lists which do not include jobs such as food workers and teachers.

Teaching union Nasuwt said it was "nonsensical".

Schools will stay closed to most pupils until the February half term unless there is a "significant" fall in Covid cases, with childcare provided to vulnerable children and the children of key workers.

According to the Welsh Government guidance, local authorities "must have regard to the list" when deciding who is a critical worker, but every child who can be safely cared for at home should be.

Find out who is classed as a key worker and read reaction from unions here.

Image source, PA Media

The wider rollout of the Oxford-AstraZeneca Covid vaccine will begin from Monday at more than 1,100 locations across Scotland.

Scotland has been given an initial allocation of more than 500,000 doses to use in January.

More than 110,000 people in Scotland have received the Pfizer-BioNTech vaccine so far.

The Oxford-AstraZeneca vaccine has already been administered in the Tayside, Lothian, Orkney and Highlands health board areas but this week will see it being used at vaccination centres across the whole country.

Those aged 80 or older will be among the first people in the community to get the Oxford vaccine and will be contacted by their health board for appointments.

Read more.

Image source, Sarah Link

A nurse who lived in a caravan for nine months to try to protect her mother from coronavirus says moving back into her house was like "winning the lottery".

Sarah Link and her husband Gary moved onto the driveway of the home they shared with her 84-year-old mother in the Black Country.

"I have cried a river in the caravan. If it wasn't for Gary, I wouldn't have got through it," Mrs Link says.

She works as a nurse at Birmingham's Queen Elizabeth Hospital.

She added: "It's getting ridiculous the cases... some people still walk around and don't believe it's real. If people came on my ward and see what I've seen..."

The pair moved back in after Mrs Link's mother received a vaccine.

"I'd do it again tomorrow. I would do it every time, I would have done anything to protect mum," says Mrs Link, who had not hugged her mother since March.

"It was like winning the lottery, waking up in a proper bed.

"We're in the warm... I wouldn't be happier if I'd won a million pounds."

You can read the full story here.

Earlier this morning, we heard from Prof Adam Finn, who sits on the Joint Committee on Vaccination and Immunisation (JCVI), which advises UK health departments on vaccines.

During his interview with Sky News' Sophy Ridge he defended the decision to delay giving people their second dose of the Covid vaccine, to allow more people to get their first dose more quickly.

It has been a controversial move.

He says these are not normal times, and strategic judgements have to be made, using current data and previous knowledge of how vaccines work.

"If you take a vaccine dose that you're otherwise saving to give to somebody as a second booster dose and put it into the arm of someone who's not immunised at all, you will start to induce protection in that second person. And with this rapidly rising epidemic at the moment, that is the imperative need," he says.

Prof Finn also said the chair of the JCVI had instructed members to come up with a plan by the middle of February for who should be prioritised for a vaccine next.

He said this would include "broader considerations" about different occupations and their relative importance to society.

Asked whether teachers could be prioritised for the vaccine, he said he could not predict who would be prioritised, but: "We will be discussing this and coming up with a plan.

"When it comes to teachers I think we all appreciate the critical role that they all play and so that really will figure in the discussions."

Regular rapid testing for people without coronavirus symptoms will be made available across England this week, the government said this morning.

The community testing regime uses rapid lateral flow tests, which can return results in 30 minutes.

The health secretary says the science is clear, and this testing helps to break the "chains of transmission", which helps people who must go out to work.

But the BBC's Andrew Marr challenges that with what he says is the scientists' assessment of their worth.

Labour's Sir Kier Starmer has accused the prime minster of being "slow into every decision" around coronavirus restrictions.

But Andrew Marr also challenged him over the closure of primary schools: "On Sunday (last week) you said specifically you didn't want to close schools. The following morning, your education spokeswoman Kate Green said schools should be the very last place to close - so you did not give a different message from the prime minister."

Starmer says: "I didn't want schools to close I'm not going to shy away from that, because of the impact that has on vulnerable children."

But the Labour leader says the PM was trying to suggest that "everything was going fine and it was the new variant that knocked us off course".

"If you look at the last nine months he's been slow into every decision," Starmer says.

"The first lockdown was slow, he was slow on protective equipment, slow on testing.

"When it came to a circuit break in the autumn, I called for a circuit break, he ridiculed that and said he wasn't going to do it, it was obviously what the medical advice was suggesting.

"Then he did it and we had a longer lockdown.

"Just before Christmas, I said to the prime minister 'this five-day mixing is going to cause real problems' and he said to me 'you're trying to cancel Christmas'."

Marr replies that on the particular decision to close primary schools "you were just as slow and just as indecisive as the prime minister".

Matt Hancock sets out to the BBC's Andrew Marr how everybody will be offered a vaccine by the autumn.

By 15 February, the goal is to have offered everybody in the top four vulnerable groups a jab, he adds.

On the other hand, "nurseries should probably close" says Labour's Sir Keir Starmer.

He tells the BBC's Andrew Marr: "I think there is a case for looking at nursery schools, we're talking to the scientists about that.

"I think people are surprised that primary schools were closed but nurseries aren't... I think they probably should be closed."

He says it is very difficult to see how restrictions can lift in any meaningful way until the vaccine programme, at least that first part of it, is rolled-out successfully.

Pressed on whether reopening was contingent on inoculating teachers, he added: "No, I don't know that it necessarily is, although if that can happen that would be a good thing.

"There are sectors where there is a very strong case for vaccination for obvious reasons, and I understand that and we are going to have that to accommodate that, quite frankly.

"At the moment, we need to focus on those who are most likely to go into hospital and tragically to die."

Matt Hancock insists schools are safe for children but says they had to close to most pupils because they still contribute to the spread of the disease.

He says there is no evidence teachers catch Covid-19 more than any other profession but children can still catch the virus and pass it on.

The health secretary defends keeping schools open for vulnerable children and the children of key workers, following reports some are at 50% of their normal capacity because of these exemptions.

He says schools need to be open for children of key workers, to allow people including NHS staff to go to work.

"Of course everybody who can work from home should work from home," he says. "But it’s really important that we still have people coming into work. "

Schools are currently shut to most pupils - except for the children of key workers, those without laptops and the vulnerable

So Matt Hancock is asked by Marr what the government's criteria is for relaxing restrictions and reopening schools.

The health secretary says there are four conditions:

• That there isn't a major new variant of the virus,
• that the vaccine rollout is proceeding effectively,
• the number of deaths is coming down
• and the amount of pressure on NHS.

He says by mid-February the government's goal is to have offered a vaccine to everybody in the top four most vulnerable groups, and it is "on track" to deliver that.

However, he adds, it still takes two to three weeks for those individuals to get immunity.

Hancock says it is not possible to be more precise on when restrictions might be lifted as it depends on how things progress.

Labour leader Sir Keir Starmer says the current lockdown rules "may not be tough enough".

He tells the BBC's Andrew Marr Show: "They are tough and they're necessary. They may not be tough enough.

"In a sense, I think the most important thing is people get that message about 'stay at home'.

"And it's up to the government to put that message out there the whole time. We've had mixed messages, I'm afraid, for the last nine months which is why we've got a problem.

"I would like to see the prime minister out there every day with a press conference making sure that message is absolutely getting through."

A virus expert says coronavirus is not likely to go away, but vaccines mean we will be able to live with it in a similar way to flu.

Professor Peter Horby tell Andrew Marr the early signs from vaccination are "very encouraging" and people should not feel like they need to "hide under the duvet".

"We've got these vaccines, they're being rolled out they're absolutely critical," he says.

"There's now three approved in the UK and - although there are some concerns and we have to be very vigilant that the new viruses don't escape immunity from the vaccine so far - the data we have is encouraging that the vaccines work just as well."

He says every virus mutates to create different strains but vaccines are updated to keep up with them.

"When there's a lot of immunity in the population, whether that's a vaccine or natural, we will see viruses emerge that escape that immunity.

"In the longer term, that will happen and we we will have to update that vaccine.

"But we do that every year with influenza so I don't think that's going to be a problem in the short term."

He says scientists do not yet know how long immunity lasts and therefore how often the population will need to be re-vaccinated.

He says: "The one virus we've managed to get rid of, smallpox, had very different characteristics to this virus... this one will not go away.

"I think we are going to have to live with it... it may well become more of an endemic.

"It will be with us all the time and may cause some seasonal pressures and some excess deaths but will not cause the huge disruption that we are seeing now."

Every adult will be offered a Covid-19 vaccine by the autumn, Health Secretary Matt Hancock says.

He adds that this will be "according to need", with the most vulnerable offered a vaccine first.

Over the last week, he says, the UK has vaccinated around two million people - more people than it did in the entirety of December.

The exact figures will be published tomorrow, he adds.

Professor Peter Horby, chair of the scientific advisory body Nervtag, explains why the new variant of coronavirus might be more infectious

Matt Hancock says the rapid lateral flow tests being rolled out for mass testing of asymptomatic people in the community are the same ones which "worked effectively in Liverpool".

However, Andrew Marr points out these tests missed 60% of positive cases in Liverpool and analysis from scientists suggested they did not provide any clear indication that mass testing had an impact on cases or hospital admissions.

The health secretary denies this and says mass testing in Liverpool saw case rates fall more sharply than in other similar areas where only restrictions were brought in.

He says community testing can help find positive cases, break the chains of transmission and make going to work as safe as possible.

Health Secretary Matt Hancock says the "vast majority of people are following the rules", adding that data suggests people are staying at home more than during the November lockdown.

“If you can do something from home and you don’t need to go outside of home to do it then you should," he urges, adding that he is working from home himself today, rather than travelling to the BBC studio.

"People need to not just follow the letter of the rules but follow the spirit as well," he adds.