The Office for National Statistics (ONS) said an estimated 618,700 people in England – one in 90 – had Covid-19 between October 25 and 31, up from 568,100 the week before.
But while the infection rate has increased in recent weeks, “the rate of increase is less steep compared with previous weeks”, the ONS said.
However, the figures do not include people staying in hospitals or care homes and are based on more than 689,000 swab tests gathered from across the UK in people with and without symptoms.
Ruth Studley, head of analysis for the Covid-19 infection survey, said: “At a national level we are seeing infections slow across England and Wales but they are still increasing.
“Within England, every region apart from the North East has shown increased levels of infection.
“The level of infection in young adults and older teenagers appears to have levelled off recently.
“However, they continue to be the most likely to be infected despite increases in all other age groups.”
When looking at new daily infections, the ONS said the rate across England appears to have “stabilised”.
There were an average of 45,700 new cases per day of Covid-19 in private homes between October 25 and 31, down from an estimated 51,900 new cases per day for the period from October 17 to 23.
This suggests the rate of new infections “appears to have stabilised in recent weeks at around 50,000 new infections per day”, the ONS said.
It comes as 64,170 deaths involving Covid-19 have now occurred in the UK, according to figures produced by statistical agencies.