More than half of the capital's 32 boroughs are now seeing seven-day infection rates below 400 per 100,000 Londoners.
The figures, for the seven days to January 25, are based on tests carried out in laboratories and in the wider community.
It shows infection rates falling in every single borough. The highest is in Brent, with a rate of 588.9 in the week to January 25 - with 1,942 new cases recorded. That is a 30 per cent fall on the rate of 838.2 over the previous seven days, when an additional 2,764 people in the borough tested positive.
The latest Public Health England figures, which have been crunched by the PA news agency, show similarly large falls have also been seen in Ealing and Hounslow, which have recently had the highest infection rates in the capital.
Meanwhile, five London boroughs - Westminster, Islington, Camden, Richmond upon Thames and Kensington and Chelsea - now have infection rates below 300 per 100,000 people.
Data for the most recent four days (January 26-29) has been excluded as it is incomplete and does not reflect the true number of cases.
Of the 315 local areas in England, 10 (three per cent) have seen a rise in case rates and 305 (97 per cent) have seen a fall.
Knowsley in Merseyside continues to have the highest rate in England, with 1,090 new cases recorded in the seven days to January 25 - the equivalent of 722.5 cases per 100,000 people.
This is down from 1,014.2 cases per 100,000 people in the seven days to January 18.
Slough in Berkshire has the second highest rate, down from 940.2 to 662.0, with 990 new cases.
Sandwell in the West Midlands is in third place, down from 902.1 to 653.7, with 2,147 new cases.
Best startups generally come from somebody needing to scratch an itch.