The Government has been accused of making the case for nationwide restrictions using figures that were “riddled with errors”.
The new study is based on around a million weekly reports on a symptom tracking app, as well as 13,108 swab tests undertaken between October and November 1.
It found that infections nationally have stopped increasing in most age groups, apart from a modest increase in the over-60s.
A separate survey by the Office for National Statistics suggested the infection rate had “stabilised” at around 50,000 new infections per day.
It estimates that 618,700 people in the community in England had Covid-19 during the week up to October 31, equating to one in 90 people.
Tim Spector, Professor of Genetic Epidemiology at King’s College London, said: “Although the number of new symptomatic cases are still high at over 40,000 daily, over the past week cases are heading in the right direction.
“The worst affected areas have shown the most improvement, but large differences between regions remain.
“Our data is an early indicator of the future NHS situation as we are two weeks ahead of hospital data and four weeks ahead of most deaths.
“So, while these population changes will take a while to work through, we believe they are a positive sign that we have passed the peak of this second wave.
“We urge everyone to respect the restrictions and help get the number of cases down as soon as possible to help the NHS, end the lockdown and get us in good shape for December.”
The study suggests the virus is in retreat across Scotland, with the R value standing at 0.9.
The number of daily new cases are still rising slowly in the South East and South West, but continue to be much lower than other regions in the UK.
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.”