Keir Starmer has called on Prime Minister Boris Johnson to implement a new national lockdown within the next 24 hours.
The Labour leader said the step was needed to curb the outbreak, which he described as "out of control".
He said: "It'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. That has to be the first step to controlling the virus."
On Sunday, Prime Minister Boris Johnson said that schools were safe and children should continue to attend next week.
However, he warned harsher Covid-19 restrictions could be on the way.
Boris Johnson hints at tougher restrictions ahead for UK
Mr Johnson, asked in a BBC interview about concerns that the tier system may not be enough to bring the virus back under control, said that restrictions "alas, might be about to get tougher".
"There are obviously a range of tougher measures that we would have to consider ... I'm not going to speculate now about what they would be."
Despite this, Mr Johnson insisted schools were safe, and advised parents to send their children in, in areas where rules allow it.
"There is no doubt in my mind that schools are safe, and that education is a priority," he said.
Much of England is already living under the toughest level of restriction under a four-tier system of regional regulations designed to stop the spread of the virus and protect the national healthcare system.
The virus is clearly out of control.
— Keir Starmer (@Keir_Starmer) January 3, 2021
It’s not good enough for the Prime Minister to hint at further restrictions at unspecified times and then do nothing.
He must put national restrictions in place within the next 24 hours.
No more dither, no more delay.
Mr Johnson sets policy for England, with rules in Scotland, Northern Ireland and Wales set by their devolved authorities.
Scottish leader Nicola Sturgeon said her cabinet would meet on Monday to discuss possible further steps to limit the spread of the virus, and ordered Scotland's parliament to be recalled.
Britain recorded 54,990 new cases of the disease on Sunday and a further 454 deaths.
The UK government's response has been heavily criticised. But the rollout of vaccines is set to accelerate on Monday with the first 530,000 doses of the newly approved Oxford/AstraZeneca vaccines ready to be administered, Mr Johnson said.
He hoped "tens of millions" would be treated over the next three months.
Millions of pupils are due to return from their Christmas holidays on Monday, and Johnson advised parents to send their children to school where they can.
"There is no doubt in my mind that schools are safe, and that education is a priority," he said.
His comments come after the UK's largest union for teachers said schools in England must stay closed for at least two weeks after the Christmas holiday
Some local authorities and unions have warned against reopening schools and have threatened to act against government advice. Others say closures also have a big negative impact on students.
"We must renew and maintain the consensus that children's time out of school should be kept to the absolute minimum," Amanda Spielman, chief schools inspector, wrote in The Sunday Telegraph.
The National Education Union also said it was unsafe for teachers to be in schools because of inadequate social distancing and ventilation, plus a lack of personal protective equipment.
The reopening of most secondary schools in England has already been delayed by two weeks.
Most primary school pupils in London will be taught remotely next week, a decision described as a “last resort” by education minister Gavin Williamson, but the government is being called on to expand the measures.
Mary Bousted, the joint secretary of the National Education Union, said all schools should be closed to stop the country’s hospitals being overwhelmed.
“We know that pupils now can transmit the virus through their homes, through to their families and into the community – they’re the most effective transmitter of the virus,” she told the BBC.
“You combine that with the new variant being up to 70 per cent more infective than the previous Covid virus, which was very infective, then it’s clear we have to do something to break the chain of rising levels of infection in our community.”
