Under the lockdown, people are only allowed to go to work if it's impossible to work from home, such as construction workers.
Britons are allowed to go out to shop for necessities including food and medicines, and to exercise, ideally once a day and locally.
Meanwhile, all schools and colleges will close from Tuesday (except for vulnerable children and those of key workers), and switch to remote learning until the middle of February.
Johnson said schools are "not unsafe" and children are "very unlikely" to be significantly affected by even the new COVID-19 variant, which is said to be 70 percent more transmissible.
But schools may "act as vectors of transmission -- causing the virus to spread between households," he said.
The latest development came as another 58,784 people in Britain have tested positive for COVID-19, marking the highest daily increase in coronavirus cases since the pandemic began in the country, according to official figures.
It was also the seventh day in a row that new cases have topped 50,000 in Britain. The country now has a total of 2,713,563 cases and 75,431 deaths.
Scottish First Minister Nicola Sturgeon also announced that Scotland would enter a new lockdown from midnight on Monday, as well as a shutdown of schools until Feb. 1.
Britain on Monday started the national rollout of the Oxford/AstraZeneca vaccine.
According to information released by the World Health Organization on Dec. 29, a total of 232 candidate vaccines are still being developed worldwide -- 60 of them in clinical trials -- in countries including Germany, China, Russia, Britain and the United States.