Data released on Friday by the Government Office for Science and the Scientific Advisory Group for Emergencies (Sage) shows the estimate for R across the UK is between 1.1 and 1.4.
R represents the average number of people each Covid-19 positive person goes on to infect.
When the figure is above 1, an outbreak can grow exponentially.
Sage also said it is concerned coronavirus cases may currently be doubling as quickly as every seven days nationally, with transmission rates potentially even faster in some areas of the country.
It said: “It’s even more important for people to remain disciplined and adhere to the current rules.”
Last week, the R number was said to be between 1.0 and 1.2.
In England, R is between 1.2 and 1.4.
The estimates for R and growth rate are provided by the Scientific Pandemic Influenza Group on Modelling (SPI-M), a subgroup of Sage.
The growth rate for the UK, which estimates how quickly the number of infections is changing day by day, is between +2% and +7%.
The most likely value is towards the middle of that range, experts advising the Government say.
The current growth rate means the number of new infections is growing by between 2% and 7% every day.
Scientists behind the data said the doubling times of coronavirus infections can be estimated from the positive growth rates.
But they also said R and growth rates are not the only important measures of the epidemic and should be considered alongside other metrics.
These include the number of new cases of the disease identified during a specified time period (incidence), and the proportion of the population with the disease at a given point in time (prevalence).
The experts also said that the weekly ONS Infection Survey has identified the same trends as SPI-M in recent weeks.
The ONS figures, also released on Friday, show an average of 6,000 people in England per day were estimated to be newly infected with Covid-19 between September 4 to 10, up from an average of 3,200 people per day for the period from August 30 to September 5.
In the East of England, the R number is 1.0-1.3, while the growth rate is between zero and plus 5%.
The R number in the Midlands is 1.2-1.5, while the growth rate is between plus 4% and plus 8%.
In the North East and Yorkshire, the R value is 1.2-1.4, while the growth rate is between plus 3% and plus 8%.
In the South East, the R value is 1.1-1.4 and the growth rate is between plus 3% and plus 7%.
The South West has an R value of 0.9-1.6 and a growth rate of between zero and plus 9%.
In London, the R value is between 1.1-1.4, while the growth rate is between plus 3% and plus 7%.
The North West has an R value of 1.2-1.5 and a growth rate of between plus 3% and plus 8%.
Over the past few months, R and growth rate estimates have been less useful in determining the state of the epidemic as the number of coronavirus cases was low.
But as cases continue to rise, experts say they now have a better estimate of these figures and this week’s data is “deemed to be reliable”.
Kevin McConway, emeritus professor of applied statistics at the Open University, described the latest figures as “undoubtedly concerning”.
He said: “Even at growth rates within the estimated range, the number of new cases could grow to high levels quickly if the interventions are not sufficiently effective.”
