Orton West & Castor, Newborough & Peakirk, Hampton Hargate, Eye & Thorney, Glinton, Northborough & Maxey and Barnack, Wittering & Wansford, all have had two or fewer cases (in the seven days up to April 16).
As the case numbers are so low, the Government does not publish case rates for those areas.
Peterborough itself has a rate of 52.4 cases per 100,000 people - the lowest rate for a number of months.
However, five area saw a rise in cases in the past seven days. The biggest rise was seen in Central Park, where there were eight more positive tests. The area also had the highest number of tests overall, with 13.
The biggest fall, other than in the six areas with two or fewer cases, was seen in Dogsthorpe, where cases fell by 10 to four.