The R rate for the UK is estimated to have risen to between 1.3 and 1.6, according to the latest data - though advisors to the government have suggested that the growth of the epidemic may be slowing.
This means that, on average, every 10 people who test positive for coronavirus will go on to infect between 13 and 16 more people.
The R rate has increased from the previous range of 1.2 to 1.5.
The Scientific Advisory Group for Emergencies (Sage), which provides the weekly estimate, said the value represents the “transmission of Covid-19 over the past few weeks due to the time delay between someone being infected, having symptoms and needing healthcare.”
Sage cautioned that while there are some early indications to suggest the growth of the epidemic might be slowing, it is too early to draw firm conclusions.
The scientific advisers said "it is still highly likely that the epidemic is growing exponentially across the country" and more data is needed to accurately assess recent changes in coronavirus transmission.
"Over the next few weeks, it will be important that we understand this in the UK and do not become complacent," they added.
This comes as the Office for National Statistics said there is “limited evidence” that the Covid-19 incidence rate in England may be levelling off following a steep rise in cases throughout August and September.
According to the ONS, there were around 8,400 cases per day between 18 and 24 September - down from around 9,600 per day during the previous week.
"There is some limited evidence that the incidence rate may be levelling off following steep increases during August and September, however the wide credible intervals mean it is too early to say", the ONS said in its latest infection survey for England, Wales and Northern Ireland.
The ONS added that there has “been clear evidence” of an increase in the number of young people testing positive for Covid-19, with the current rates highest in teenagers and young adults.
More to follow