The number of people infected with coronavirus in homes in England has fallen to 5,600 a day, from 8,000 last week.
The estimate is based on swab tests of 19,000 people in 9,000 households by the Office for National Statistics.
Some scientists have said reaching a low level of cases was key to easing the lockdown further.
Test and trace programmes were introduced in England and Scotland last week to track contacts of new cases.
The ONS study of adults and children in private households suggests there are 39,000 new infections a week in England.
It estimates that one in 1,000 people had coronavirus in the community between 17 and 30 May, not counting those staying in hospitals or care homes.
This is down from last week’s estimate of one in 400.
The figures for England are based on a small number of positive swab tests – 21 people in 15 households – so there is some margin for error.
But because everyone in the household is tested, whether they have symptoms or not, the results are thought to be a more accurate picture of how many people are currently infected by the virus.
Based on last week’s ONS estimate of 8,000 daily infections, some scientists advising the government warned against relaxing lockdown measures too quickly.
They said waiting until cases fell further would make the virus easier to control, and give test and trace programmes more chance of succeeding.
On the basis of this study, “the number of people in England testing positive has decreased in recent weeks”, the ONS says.
The results show that only 29% of those who tested positive for coronavirus said they had any symptoms at the time of the test.
Those working outside the home were more likely to test positive for virus than home-workers, with healthcare workers and social care workers at highest risk of being infected.