The update comes amid growing concern over a new variant of COVID-19 which appears to be causing a dramatic uptick in infections in London and the southeast of England, prompting the prime minister to enforce new Tier 4 restrictions.
Restrictions have also been increased in Wales and Scotland.
Boris Johnson said during a Downing Street news briefing on Saturday that the new strain could raise the R number - the rate of transmission - by "0.4 or greater".
Documents discussed by government advisers on Friday show 0.4 to be at the lower end of the estimate.
A summary of the New and Emerging Respiratory Virus Threats Advisory Group (NERVTAG) meeting said: "Studies of correlation between R-values and detection of the variant: which suggest an absolute increase in the R-value of between 0.39 to 0.93."
It also said that the mutation had seen an "exponential growth" during the recent national lockdown.
The new strain, which is up to 70% more transmissible, has been found in every part of the UK except Northern Ireland, an expert has told Sky News.
In England alone, 32,155 new cases were announced on Sunday, compared to 22,775 on Saturday.
Dr Yvonne Doyle, medical director at Public Health England, said the "sharp and sudden increase" in new cases on Sunday was of "serious concern".
"Most of the new cases reported today are concentrated in London and the South East, although it is too early to tell if this is linked to the new variant," she said.
"What we do know is that the way to control this virus is the same, whatever the variant. It simply will not spread if we avoid close contact with others.
"Wash your hands, wear a mask, keep your distance from others, and reduce your social contacts.
"By working together we have tackled this virus before. By holding the line over the next few weeks, it is possible we can do so again, as we continue to roll out the vaccine to the most vulnerable."
Another 326 deaths within 28 days of a positive test were recorded across the UK on Sunday, taking the total number of coronavirus-related deaths to 67,401.
The number of cases now stands at 2,040,147.
Health Secretary Matt Hancock has warned that the new strain of COVID-19 is out of control and people need to behave as if they already have the virus, especially in the new Tier 4 areas of England.
The five-day Christmas bubble period has been reduced to just Christmas Day for England, Wales and Scotland - and scrapped completely for areas in England under new Tier 4 rules - but remains in Northern Ireland.
A US gymnast's routine celebrating "black excellence" has gone viral, with millions of views on social media.