The R number in the UK has risen to between 0.9 and 1.1, the government's scientific advisory group (SAGE) says.
The R number is a measure of how many people on average each infected person transmits the virus to.
It is an increase on an estimated range of 0.8-1.0 last week, compared with 0.8-0.9 a fortnight ago.
SAGE also said the rate of coronavirus growth may still be rising.
The latest growth rate for the UK is between minus 3% and plus 1%, an increase from between minus 4% and minus 1% last week.
This indicates the number of new infections is somewhere between shrinking by 3% and growing by 1% every day.
Scientists at SAGE say the most likely value is towards the middle of the range.
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Because the data used to calculate R and growth rate reflect the situation from a few weeks ago, recent changes in transmission are not yet fully reflected in the estimates
Experts also stress the figures are estimates and that there is a high degree of uncertainty around them.
It may take between two to three weeks for the changes in the spread of COVID-19 to be reflected in the estimates, due to a time delay between initial infection and the need for hospital care.
But the scientists said models that used testing data, which have less of a time delay, indicate higher values for R in England.
In England, the R is estimated to be between 0.9 and 1.0, and the growth rate is minus 3% to zero.