The number of cases fell from 2,335 in the seven days from September 4 to 10, to 1,699 in the period from September 11 to 17.
With medical and scientific chiefs warning that the virus is spreading fast, the number of positive cases would be expected to rise.
The data could suggest hundreds of cases in the capital are going untraced, which risks fuelling the spread of the disease if these individuals are continuing to go to work and socialise rather than self-isolate.
Another possibility is that the fall in cases reflects the virus retreating after the rule of six restrictions on social gatherings was introduced last week.
Whitehall officials, however, are said to no longer fully trust the testing data to show how the epidemic is growing and instead are relying increasingly on other information, such as Covid-19 hospitalisations and coronavirus-related calls to the NHS.
Infection rates are continuing to rise in a small number of hotspot boroughs, including Redbridge, which has reached 42.6 cases per 100,000 over a seven-day rolling average, up from 36.4 the previous week.
The rates are falling in other areas, including Hackney and the City of London, Hounslow, Enfield, Tower Hamlets, Hammersmith and Fulham, Ealing, Kensington and Chelsea, Lambeth and Croydon.
The Department of Health insisted testing is available in London and urged people to seek a test only if they have Covid symptoms or were otherwise eligible. However, shadow health minister Justin Madders stressed the London figures showed a “hugely worrying situation”.
Rates in individual boroughs can be significantly affected by an outbreak, for example in a care home, as the number of confirmed cases is still low in the city, but had been rising quickly.
Anne Longfield, the children’s commissioner for England, also warned that the Government must urgently improve its testing regime.
She said: “The PM and chief medical officer have said schools are a priority. But they can’t now throw those achievements away by not having tests in place.”