Sir Keir Starmer has called for a “round the clock” vaccination programme to tackle the rise in Covid cases.
As part of a televised speech, the Labour leader said the government needed to deliver “millions of doses a week by the end of the month”.
He said there were “serious questions for the government to answer” over the timing of the lockdown in England, but Labour would support the restrictions.
Boris Johnson said daily vaccination figures would be published from Monday.
The prime minister has also promised the four most vulnerable groups of people across the UK will receive their first dose by mid-February.
Both the PM and Scotland’s First Minister, Nicola Sturgeon, have announced lockdowns this week.
Wales has been in a national lockdown since 20 December and Northern Ireland entered a six-week lockdown on 26 December.
England’s lockdown will become law from 00:01 GMT Wednesday and MPs will return to the Commons later that day to vote on the measures retrospectively.
The restrictions come into force as the number of new daily confirmed cases of coronavirus in the UK topped 60,000 for the first time since the pandemic started.
On Tuesday, 60,914 had tested positive in the previous 24 hours and a further 830 people had died within 28 days of a positive test.
In an address to the nation on BBC One, in response to Boris Johnson’s televised address on Monday, Sir Keir said the UK had reached a “critical moment in our fight against coronavirus”.
The Labour leader said people were “angry at the mistakes the government has made” and ministers needed to answer questions on why they did not act sooner over locking down England.
He stressed that Labour would continue to hold the government to account, but added: “Whatever our quarrels with the government and with the prime minister, the country now needs us to come together.
“At this darkest of moments, we need a new national effort to re-kindle the spirit of last March – to come together and to do everything possible to stay at home [and] to protect the NHS and save lives.”
Sir Keir reiterated that Labour would support the new lockdown when it comes to the retrospective Commons vote on Wednesday and “join in this national effort”.
But he called for the government to use the lockdown to establish “a massive, immediate, and round the clock vaccination programme” to “deliver millions of doses a week by the end of the month in every village and town, every high street and every GP surgery”.
The Labour leader added: “This is now a race between the virus and the vaccine and if we pull together as a nation, we can win.
“We need a new contract between the government and the British people: The country stays at home, the government delivers the vaccine.”
‘Jab by jab’
Earlier at a Downing Street press conference, Mr Johnson said more than 1.3 million people across the UK had now been vaccinated with either the Pfizer and AstraZeneca vaccines.
The figure included 23% of over-80s in England – part of a programme Mr Johnson said aimed to save “the most lives the fastest”.
The PM said there will “still be long weeks ahead”, but that he wanted to give “maximum possible transparency” about the vaccination roll-out.
More details will be announced on Thursday, with daily updates starting on Monday, “so that you can see day by day and jab by jab how much progress we are making”, he added.
Asked whether the target could be met, Chief Medical Officer for England, Professor Chris Whitty, said the timetable was “realistic but not easy”.