The upper-tier local authority reported just six cases from June 22 to 28, up to 15 in the following week to July 5.
Southampton and Hertfordshire saw an increase of eight cases each week on week.
In Southampton, there were just two reported cases from June 22 to 28, while the region reported 10 confirmed cases in the following week.
By comparison, Hertfordshire reported 29 cases the first week, as opposed to 37 cases in the latter week.
While the figures are no way comparable to the hundreds of new cases seen in Leicester, the rise in cases is still interesting to note.
The Government has confirmed it will monitor the situation in areas where a sharp rise in cases has been reported to decide if further local lockdown will be appropriate.
A Whitehall source said: “We’re monitoring the situation hour by hour and won’t hesitate to lockdown other places if necessary.
“People must be sensible and observe social distancing rules or their home town or city could be next.”