Imperial College London
Latest data shows 15% drop, but conflicts with samples of asymptomatic cases.
Government adviser Neil Ferguson said early release from restrictions put on millions of people “not looking optimistic”.
There was an even more dramatic drop in the north of the country, researchers found.
"The risk of having a severe outcome from Covid-19 far outweighs any theoretical risk of a vaccine," Robin Shattock told BBC Question Time.
Research by Imperial College London suggests that just 4.4% of people in England had antibodies at the end of September.
The country's largest Covid-19 study, by Imperial College London and Ipsos MORI, found the virus has been doubling every 29 days.
Nicola Sturgeon is due to unveil fresh measures on Wednesday but "final decisions" have yet to be made.
It comes as reports say health chiefs fear a second wave of coronavirus could take hold in the capital.
“It’s a bit like water seeping through a dam, it starts as a trickle and if you don’t do something about it it can turn into a real cascade.”
The epidemiologist's warning comes after Boris Johnson imposed new lockdown measures to fight a spike in cases.