The R number in the UK is estimated to have gone up to between 1.1 and 1.2, according to the SAGE group of government advisers.
The growth rate of COVID-19 is therefore estimated to be between 1% and 4%.
Last week, the number was put at 0.9-1.0, with a growth rate of -2% to 0% per day. And when England emerged from November's lockdown earlier this month, the number was 0.8-1 - the lowest since August.
The R number is the rate at which the infection is passed on, meaning the latest data estimates that 10 people are passing the virus on to another 11 or 12.
Experts from SAGE gave the overall estimate for the UK but their estimates also show a variations across regions.
The English regions with the lowest R number, according to the latest data, are the North East and Yorkshire and the North West, where the number is 0.9 to 1.1.
England's regional R numbers are:
East of England - 1.1 to 1.3
London - 1.1 to 1.3
Midlands - 1 to 1.2
North East and Yorkshire - 0.9 to 1.1
North West - 0.9 to 1.1
South East - 1.1 to 1.3
South West - 0.9 to 1.2
The updated R number will do nothing to reassure those concerned about the impact a relaxation of restrictions over Christmas may have on the pandemic.
The prime minister is advising people who plan to form "Christmas bubbles" next week to start minimising contact with those outside their household from today, but top nurses and scientists are among those who have warned of a significant spike in cases, hospitalisations and deaths in the New Year.
It comes as data shows as many as one in 95 people tested positive for COVID-19 last week.
England, Wales and Scotland saw a rise in the percentage of the population with the virus in the week of 6-12 December. Numbers in Northern Ireland no longer appear to be decreasing.
That week's figure of 567,300 is a rise from 481,500 people - or one in 115 - on the previous week.
The figures from the Office for National Statistics do not include people in hospitals, care home or other institutional settings.
Analysis: Epidemic is picking up speed and underlines need to be cautious at Christmas
By Thomas Moore, science correspondent
The official R number - the measure of the virus's spread - confirms that the epidemic is picking up speed.
It's up on last week, continuing the acceleration we have seen since lockdown was lifted at the start of December.
The government Office for Science says the epidemic is growing at between 1% and 4% every day.
But there are big regional variations, with the biggest increases in the East of England and London.
There, the epidemic is growing up to 6% a day, which is alarmingly high as we go into the Christmas period.
It will underline the concern of many scientists that the household mixing permitted under the government rules will lead to a further, explosive surge in cases, hospital admissions and deaths early in the New Year.