All schools and colleges will close to most pupils and switch to remote learning from Tuesday.
Boris Johnson urged people to follow the rules immediately amid surging cases and patient numbers.
He said those in the top four priority groups would receive a first vaccine dose by the middle of next month.
All care home residents and their carers, everyone aged 70 and over, all frontline health and social care workers, and the clinically extremely vulnerable will be offered one dose of a vaccine by mid-February.
Speaking from Downing Street, Mr Johnson said all the new measures would last until at least the middle of February.
He said the weeks ahead would be the "hardest yet" as a new more infectious variant of the virus spreads across the UK.
The PM added that he believed the country was entering "the last phase of the struggle".
Hospitals are under "more pressure from Covid than at any time since the start of the pandemic", he said.
And he reiterated the slogan used earlier in the pandemic, urging people to "stay at home, protect the NHS and save lives".
Photo supplied BBC TV Caption: Boris Johnson says the spread of the new variant is "both frustrating and alarming"