About 7% of people in England have been infected with coronavirus, antibody tests on a random sample of households suggest.
"Herd immunity is not worth worrying about" at that level, say experts involved in the Office for National Statistics study.
The results are based on blood samples taken from 885 people from private households after 26 April.
The number of people who have had the virus has never been clear.
This is because only a small proportion of people with symptoms have been tested and many more may have had no symptoms at all.
Using antibody tests, the ONS study estimates that around one in 15 people have had the virus. Previous estimates have indicated it could be anywhere between 5% and 20%.
The findings indicate "that the majority of the population are unlikely to have been infected," says Prof Lawrence Young, professor of molecular oncology at Warwick Medical School, University of Warwick.
These tests detect antibodies which form in the blood when the body fights infections such as Covid-19.
It takes around two to three weeks for them to appear and once a person recovers, they stay in the blood at low levels.
Antibodies help to prevent someone being infected by the virus again, but scientists still don't yet know how long this protection lasts.
How many have the virus now?
The same household survey carried out another kind of test - a swab test to detect the presence of the virus - on many more people.
Based on tests of nearly 19,000 people living in 9,000 households in England, roughly 133,000 people are estimated to be currently infected with the virus - 0.24% of the population.
Between 11 and 24 May, the swab tests of 36 people came back positive from the snapshot survey of households.
Although the figures are small, figures for previous weeks going back to the end of April were similar, suggesting that cases in the community are not rising.
The ONS says this means numbers with the virus are "relatively stable".
But this doesn't necessarily mean the reproduction (R) number is one or less, since the findings are just one piece of evidence considered by the government's scientific advisers.
From the numbers testing positive, the ONS estimates there are 54,000 new coronavirus infections per week in England, or around 8,000 a day.
This is nearly four times as many as the government's daily figures suggest - and is likely to be the result of infections going undetected in people with mild symptoms or none at all.
The results of the swab tests also found that healthcare workers and social care workers who have direct contact with patients are more likely to test positive than other workers.
People working outside the home showed higher rates of positive tests than those working from home.
Of those who tested positive, around 30% had symptoms in the days around the day they were tested.