Boris Johnson, 56, has urged people to get inoculated and said England’s roadmap out of lockdown was “on track”.
He said there was “no change” to the plan despite a drop in vaccine supply.
Several European countries are to resume using the AstraZeneca jab after the European Medicines Agency (EMA) confirmed it was “safe and effective”.
The regulator reviewed the vaccine amid fears about blood clots, but said it was “not associated” with a higher risk and the benefits outweighed any risks.
Mr Johnson told a Downing Street conference on Thursday that the AstraZeneca jab was safe but “the thing that isn’t safe is catching Covid, which is why it is so important that we all get our jabs as soon as our turn comes”.
The prime minister was himself treated in hospital for Covid-19 in April 2020 during the first wave of the pandemic.
“The way to ensure this [lockdown easing] happens is to get that jab when your turn comes, so let’s get the jab done,” he said.
Prof Chris Whitty, chief medical officer for England, said there were “anecdotal reports” of small numbers of people not turning up for vaccine appointments following the controversy over the AstraZeneca jab in Europe.
But he said he expected many of those would decide to get the jab after “a pause for thought”, adding that Covid was still a “very dangerous disease”.
“People dying, people getting significant blood clotting problems, that’s one of the risks of Covid, people having long-term physical and mental effects from Covid,” he said.
Mr Johnson said England’s progress towards leaving restrictions on daily life was “unchecked” by vaccine supply issues, where fewer doses have arrived from India than initially expected.
There were often delays with vaccine rollout programmes, he said, and he stressed the Indian government had not stopped any exports.
Prof Neil Ferguson, from Imperial College London, said while the delay was “disappointing” he did not think it would have “an enormous effect” on the rollout.
However, he warned the UK needed to keep variants of concern “at bay” until it could update vaccines and roll them out to the whole population.
Prof Ferguson, who is a member of the government’s SPI-M modelling group, told BBC Radio 4’s Today programme there should be particular concern about cases being imported from France, where infection levels are increasing.
He added that 5-10% of cases in France were the South African variant, which is of concern because it could be more resistant to current vaccines.
But Prof Ferguson suggested that adding France to the “red list” of countries, from which arrivals are required to quarantine in a hotel, would not be “practical” given the amount of essential trade and commerce between the UK and France.
Instead he said “a more bespoke arrangement” to mitigate the risks, perhaps including testing of arrivals, would be needed.