Sir Keir said national restrictions have to be "the first step towards controlling the virus".
He said: "There’s no good the prime minister hinting that further restrictions are coming into place in a week, or two or three.
"That delay has been the source of so many problems.
"So, I say bring in those restrictions now, national restrictions, within the next 24 hours."
ITV News Political Correspondent Dan Hewitt reports that Sir Keir Starmer wants a national lockdown like November, not March, with the national 'Stay At Home' message brought back. Schools should be “the last to close”, a senior source told him.
His comments come just hours after Boris Johnson signalled that England's current Covid tier system could be tightened, with tougher measures likely to come in.
Mr Johnson also urged parents to send their children to primary schools that are open in England on Monday, adding: "There is no doubt in my mind that schools are safe".
The prime minister told BBC One's The Andrew Marr Show: "Yes, absolutely they should in areas where schools are open."
Meanwhile Sir Keir said: "It is inevitable more schools are going to have to close.
"And the Government needs a plan on children’s learning but also for working parents."
Pressure is mounting on the government from both sides on whether children in England should return to school as normal following the Christmas holiday amid soaring Covid-19 rates.
Mr Johnson's calls for children to return to school were echoed by Ofsted chief inspector Amanda Spielman who has warned that children’s education cannot be “furloughed” for months while Covid-19 vaccinations are rolled out and the country waits for coronavirus cases to subside.
Writing in the Sunday Telegraph, the head of England's schools watchdog said that time away from school should be kept to an "absolute minimum".