The Labour leader told MPs in the the House of Commons, that the current lockdown in England is not "strong enough".
Japan's health ministry said on Sunday it had detected a new strain of COVID-19 in four travellers from Brazil's Amazonas state which featured 12 mutations, including one also found in highly infections variants discovered in Britain and South Africa.
"This is the toughest of times, but we can see the way forward".
"We will be going to 24/7 as soon as we can", he told MPs.
Earlier, Health Secretary Matt Hancock told Sky News it was "impossible to know" how long current COVID restrictions might be in place for.
"We already have tough measures to protect this country from new infections coming in from overseas and we're taking steps to do that with respect to the Brazilian variant", he added.
The Labour leader, Sir Keir Starmer has asked why Boris Johnson was "slow to act" as during December infections surged.
Mr Hancock earlier questioned whether there would be demand for a round-the-clock vaccination operation. With 2.6 million first vaccine doses administered so far, the government needs more than 2 million vaccinations a week to hit its target. Mass vaccination centers are now open from 8 a.m.to 8 p.m., 7 days a week.
Tom Keith-Roach, president at AstraZeneca UK, said: "We are scaling up very rapidly and this will happen imminently to releasing two million doses a week".
Britain has so far given vaccinations to around 2.4 million of its most vulnerable citizens, and the government has set a target of 15 million by the middle of next month.
- A national voucher scheme for free school meals in England will relaunch next week after issues with food parcels for children not in class were highlighted by campaigners including footballer Marcus Rashford and cook Jack Monroe.
Addressing senior MPs on the House of Commons liaison committee, the United Kingdom prime minister also revealed his government is concerned about another new viral strain which has emerged in Brazil and is considering further travel restrictions on arrivals from the country.
In reply to Sir Keir, Mr Johnson said: "We keep things under constant review and we will continue to do so".
Johnson also said on tougher restrictions brought in last week were starting to have an effect on the spread of COVID in some parts of the country, cautioning that it was still early days.
The picture in the South and East is less certain, and, while rates may have peaked in some areas it will be several days before a clear trend - either up or down - becomes evident.