There were 41 new cases in Hackney and the City of London last week – 24 more than the previous week.
The 25 new cases in Barnet were 12 more than the week before.
In 17 of the 32 London boroughs, new cases were lower than the previous week’s number.
Newham’s 22 cases were 11 more than in the previous week, but in another eight boroughs where there had been a rise, it was five or less.
In three boroughs, the number was the same as the week before.
The difference in new cases could reflect the level of testing rather than incidence of the disease.
Meanwhile, the Board of Deputies reported that UK Jewish deaths from coronavirus had risen to 506 by last Friday, up two from the previous week.
The UK death toll from the disease stands at 45,422, according to government figures based on positive tests for coronavirus.
But data from the Office for National Statistics, which counts cases where coronavirus has been registered as a cause of death, puts the number above 55,000.
On Wednesday, Hackney council tweeted a video message from the Jewish emergency medical service Hatzola advising anyone showing symptoms of the virus to get a test.
A mobile test unit will be in Stamford Hill this Sunday and the following Sunday.