Coronavirus vaccines have prevented 10,400 deaths in people aged 60 and over, according to analysis by Public Health England (PHE).
The figures, which cover the period from 8 December to the end of March, suggest more than 9,000 likely fatalities were prevented in those over 80.
PHE said it had used "real-world data" to assess how effective the jabs are, adding that there is "increasing evidence that vaccines help to reduce transmission".
Taking that into account, it is plausible that an "even higher number of deaths will have been prevented by the vaccination programme", it added.
The analysis "compared the observed number of deaths with the number of deaths that would have been expected if the vaccine hadn’t been given during this time period".
PHE added: "To allow for the time taken to develop an immune response to vaccination, the analysis assumed it would take 31 days before the effect of vaccination on deaths is observed."
PHE’s head of immunisation, Dr Mary Ramsay, said the new report was "further evidence that the COVID-19 vaccinations are continuing to prevent hundreds of deaths every day".
Reacting to the figures, Boris Johnson tweeted: "The science is clear: vaccines save lives."
The prime minister added: "It’s important that you book your jab when the NHS contacts you."
It comes after it was announced Britons aged 18-29 will be offered an alternative to the Oxford-AstraZeneca vaccine after 79 people developed blood clots within days of getting the jab.
There is a possible link between the Oxford vaccine and "extremely rare and unlikely to occur" blood clots with lowered platelets, the Medicines and Healthcare Products Regulatory Agency (MHRA) concluded.
Younger people are much less likely to die from COVID-19, so the Joint Committee on Vaccination and Immunisation (JCVI) decided it was safer to advise that age group are offered a different jab, where possible.
Health Secretary Matt Hancock said: "All three of our approved vaccines have been deemed safe and effective by our world class independent medicines regulator."
He added that the PHE figures "show why it’s so vital that people get their second dose too".
Earlier this week a 24-year-old carer, Elle Taylor, became the first person in the UK to receive the Moderna vaccine.
Meanwhile, it looks likely that the NHS will reach its latest immunisation target with ease.
It has been aiming to administer 32 million first doses by next Thursday.
As of yesterday, 31.81 million first jabs had been given – and there is still just under a week to go.