It comes after the Department for Education (DfE) announced secondary pupils would also be required to wear face coverings at school.
Ministers are currently assessing whether tougher Covid-19 restrictions are necessary, amid reports of massive pressure on the NHS.
What has been announced for schools
Education Secretary Nadhim Zahawi announced the new measures on Sunday (2 January).
He said they had been introduced because the Government wanted to “offer some reassurance” and ensure that “face-to-face teaching [would] continue to be the expected norm”.
Mr Zahawi added that schools and colleges would also have greater access to tests that could be taken by pupils at home via a “different supply route” to the one used for tests for the general public.
As well as offering tests and enforcing mask wearing, DfE has also pledged to provide educational establishments with an additional 7,000 air cleaning units to improve ventilation in teaching spaces.
Meanwhile, 12 to 15-year-olds are being encouraged to have their second Covid vaccine and 16 to 17-year-olds are now eligible for a booster dose.
Mr Zahawi also told headteachers to consider merging classes or sending groups of children home if the number of staff off work due to Covid reaches critical levels.
Speaking to BBC Breakfast this morning, the Education Secretary said: "The painful lesson we learnt was when children weren’t in school, the impact on their mental health and, of course their education, was quite substantial.
"Which is why I’m so determined, as is the Prime Minister, to make sure education remains open and children are in the best place when they’re in the classroom, with their friends, learning in front of a teacher."
And speaking to Sky News, he said the new measures would not be in place “for a day longer than we need it”.
What has the reaction been?
While there has not been much reaction to the testing announcement, the news that masks would have to be worn in school has had a mixed reaction.
Conservative MP Robert Halfon, who chairs the Commons Education Select Committee, said he feared the move could damage children’s mental health.
But Wes Streeting, Labour’s shadow Health Secretary, said he would rather have face coverings worn in classrooms than children stuck at home.
Leading teaching and education unions said the face mask rules were “overdue” and called for them to be made “a requirement”.
National Education Union joint general secretary Dr Mary Bousted also described the air purifier announcement as “completely inadequate” given there were “over 300,000 classrooms in England”.
It all comes as a further 137,583 lab-confirmed Covid cases were recorded in England and Wales as of 9am on Sunday, according to official figures.
This was down on the 162,572 cases recorded in England alone on Saturday.
It was reported on Sunday (2 January) that United Lincolnshire Hospitals NHS Trust had declared a “critical incident” linked to “extreme and unprecedented” staff shortages.
And in Wales, Swansea’s Morriston Hospital said it could provide only a “limited service” in its emergency department over the bank holiday weekend due to staffing pressures “worsened by Covid”.
The chief executive of NHS Providers Chris Hopson said that staff were working “flat out” and that the NHS was under “arguably more pressure” compared with this time last year.
Figures published by the Office for National Statistics show there have now been 174,000 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
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