The UK is facing a “perilous moment” in the pandemic and must guard against complacency, the PM has said, as he announced a total of 2.4 million vaccinations have been given so far.
Visiting a vaccination centre in Bristol, Boris Johnson said: “We have a really tough fight on our hands.”
It comes as seven mass inoculation centres have opened in England.
And England’s chief medical officer has warned the next few weeks will be “the worst” of the pandemic for the NHS.
Prof Chris Whitty has urged people to minimise unnecessary social contacts.
Sunday’s figures showed another 563 deaths in the UK within 28 days of a positive Covid test, and another 54,940 cases. There are also more than 32,000 people in hospital with coronavirus, the latest data shows.
Meanwhile, the government has set out its plans to immunise tens of millions of people by spring.
Health Secretary Matt Hancock will lead a news conference on the vaccine delivery plan later.
Speaking at Ashton Gate Stadium, Mr Johnson said 2 million people have already received a Covid vaccine across the UK, which means around 400,000 people have had two doses.
He said “roughly” 40% of over-80s have been vaccinated, and 23% of elderly residents in care homes.
Under the vaccine delivery plan, the government has pledged to carry at least two million vaccinations in England per week by the end of January, which it says will be made possible by rolling out jabs at 206 hospital sites, 50 vaccination centres and around 1,200 local vaccination sites.
The plan also reiterates the government’s aim of offering vaccinations to around 15 million people in the UK – the over-70s, older care home residents and staff, frontline healthcare workers and the clinically extremely vulnerable – by mid-February.
But the prime minister warned the vaccination programme was in a “race against time” because of the pressure the NHS was under.
And he said it was “a very perilous moment because everyone can sense the vaccine is coming in – my worry is that will breed false complacency”.
Asked whether the government would introduce stricter lockdown rules, Mr Johnson said ministers would keep restrictions “under constant review”, adding: “Where we have to tighten the rules we will.”