England’s estimated R number has fallen slightly to between 0.8 and 1.
Last week, it was between 0.8 and 1.1.
An R number – or reproduction number – between 0.8 and 1.0 means on average every 10 people infected with COVID-19 will infect between eight and 10 others.
When the figure is above 1, an outbreak can grow exponentially but when it is below 1, it means the epidemic is shrinking.
Meanwhile, the daily growth rate of infections in England is estimated at between -4% and 0% per day, according to the figures from the United Kingdom Health Security Agency. That suggests prevalence of the virus is shrinking.
It is down on last week when cases were believed to be growing by between -3% and 1%.
The estimates represent the situation two to three weeks ago, due to the delay between someone being infected, developing symptoms, and needing healthcare.
However, levels of coronavirus infection remain high across much of the UK.
Separate figures show the rate of new cases of the virus is currently rising in all four nations, suggesting the sharp fall in COVID-19 cases that had been under way since mid-July has now come to an end.
Prevalence is highest in Northern Ireland, according to the Office for National Statistics (ONS).
About one in 55 people are estimated to have had Covid-19 in the country last week – unchanged on the previous week and the highest level since late January.
This is followed by England, where the number is around one in 75 people, also unchanged from the previous week.
The ONS said that while the percentage of people testing positive for coronavirus in England “continued to be high”, estimates suggest “an overall decreasing trend over the past two weeks”.
In Wales, where around one in 220 people are estimated to have had the virus last week, the trend is described by the ONS as “uncertain”. It is broadly unchanged on one in 230 in the previous week.
Scotland was the only area to see a fall, with ONS estimates suggesting around one in 190 people had Covid-19 in the week to August 7, down from one in 120 in the previous week.
According to the latest Government data, England recorded 301.6 new cases per 100,000 people in the seven days to August 8, up week-on-week from 282.3.
In Wales the rate is up week-on-week from 141.6 to 155.7, while Scotland’s rate has climbed from 143.7 to 156.1.
In Northern Ireland the rate has risen from 440.8 to 475.5 – the highest for any of the four nations.
Professor James Naismith, director of the Rosalind Franklin Institute, said he expects to see a fourth wave in the wake of eased restrictions and with the return of schools and people moving indoors after the summer.
He said: “I would expect to see a rise in cases, a fourth wave.
“I do not know the size of any new increase nor do I put much faith in those that claim with certainty to ‘know’.”
But Prof Naismith added: “I know that any significant rise in cases will lead to more long Covid-19 and increase the pressure on the NHS.”
He called for a “more effective (vaccine) campaign to encourage the take-up amongst the hesitant”, saying jabs are safe and effective and had already saved tens of thousands of lives.
Prof Naismith added: “The more vaccinated people, the smaller any fourth wave.”
It comes as more than 40 million people are now fully vaccinated against COVID in the UK, according to government data.