A further 1,610 people have died in the UK within 28 days of a positive Covid test - the biggest figure reported in a single day since the pandemic began.
It means the total number of deaths by that measure is now above 90,000.
A total of 4,266,577 people have now received the first dose of a vaccine, according to the latest government figures.
Another 33,355 positive Covid cases have been recorded - less than half the peak figure of 68,053 on 8 January.
It is the lowest number of daily cases seen since 27 December - before the start of England's third nationwide lockdown.
Dr Yvonne Doyle, medical director at Public Health England, said: "Whilst there are some early signs that show our sacrifices are working, we must continue to strictly abide by the measures in place."
She said reducing contact with others and staying at home will lead to "a fall in the number of infections over time".
The figures come as new estimates from the Office for National Statistics show about one in 10 people across the UK tested positive for Covid-19 antibodies in December - roughly double the October figure.
The rising number of deaths was to be expected, sadly, after the surge in cases during December.
And it is likely that the coming weeks will see figures even higher than this.
Today's numbers are, though, inflated by the fact that delays in registering deaths over the weekend tends to lead to higher figures being reported on Tuesdays and Wednesdays.
On average, the UK is recording more than 1,100 deaths a day.
To put that in context, at Christmas it was less than half of that.
But there are two rays of hope in the daily update.
Firstly, the number of cases is below 40,000 for a third day in a row. Just two weeks ago we saw a few days above 60,000.
That means in the coming weeks we should start to see fewer people in hospital and eventually fewer deaths.
The number of vaccinations also continues to rise.
It seems unlikely the NHS will manage its target of two million doses a week just yet.
But each increase at least takes us one step closer to getting on top of the virus.
Meanwhile, NHS England said 400 military personnel were now assisting in hospitals in London and the Midlands, as wards face "unprecedented pressure".
On Monday, Prof Stephen Powis, national medical director for NHS England, said it would be "some time" before the vaccination programme begins to reduce pressures on hospitals.
And in other developments, Health Secretary Matt Hancock has said he is self-isolating after being alerted by the UK's NHS Covid-19 app .that he had been in close contact with somebody who tested positive.
He said self-isolation was "perhaps the most important part of all the social distancing" and urged others to do the same if contacted.
The previous highest number of daily deaths was last Wednesday, when 1,564 deaths were recorded.
Tuesday's figure brings the total number of deaths recorded during the pandemic in the UK to 91,470.
These government figures count people who died within 28 days of testing positive, but there are other ways of measuring the total number of deaths.
Another method is to count all deaths where coronavirus is mentioned on the death certificate. That figure has now officially reached 95,829, although that is only measured up to 8 January.
The UK has recorded the fifth-highest number of deaths globally, according to Johns Hopkins University - behind the US, Brazil, India and Mexico.
Labour leader Sir Keir Starmer tweeted: "British people are paying the price for the government's serial incompetence."