While one area in Fareham reported a 154 per cent increase in Covid rate, Hayling Eastoke saw a 59 per cent decrease in cases.
Figures are calculated by comparing the Covid rate per 100,000 people on August 31 and on September 7, the seven day period in which pupils across the country returned to school.
Data is provided on a neighbourhood level, called Middle Layer Super Output Areas.
However, Councillor Sean Woodward, leader of Fareham Borough Council wants to reassure residents that there is no cause for alarm.
He said: ‘We are talking about very small numbers of people - when we break it down, there’s only about 15 people (infected) in the whole of the west of Fareham.
‘Because the numbers are so small, it has a disproportionate effect when we only look at the percentage.
‘There is no “west of Fareham pandemic”.’
Other Fareham areas which reported higher Covid rates include Stubbington (an increase of 71 per cent), Warsash and Fareham Common (both 50 per cent), and Fareham North West (35 per cent).
Locks Heath, however, saw a decrease in Covid rates of 38 per cent, while Swanwick and Sarisbury Green reported 35 per cent fewer cases, and Fareham Town and Cams Hill saw a 24 per cent decrease.
Cllr Woodward said: ‘There are increases in some parts and decreases in numbers, and I would expect some sort of increase with the schools, a few more infections.
‘I wouldn’t think it was anything to hugely worry about.’
The UK’s chief medical officers are recommending vaccinating children aged 12 to 15.
Cllr Woodward added: ‘Don’t be alarmed - get vaccinated.
‘I’m absolutely delighted with the vaccine programme so far - I have very great praise for the surgeries and the community hospital for the military-style operation they’ve been running for many months.’
Several areas across Portsmouth saw a surge in cases, including Southsea Fawcett Road (a 52 per cent increase between August 31 and September 7, Fratton Kingston (a 50 per cent increase), Wymering (38 per cent), Somers Town (32 per cent), and Southsea Prince Albert Road (28 per cent).
However, several locations in the city also saw a downturn in Covid cases - coronavirus rates in Drayton and Farlington have halved, with 53 per cent fewer cases reported in the same period.
Areas which also saw a reduction in Covid rates during this time include Paulsgrove East (which saw a 42 per cent decrease), Southsea West (41 per cent), and Milton (31 per cent).
In Gosport, Covid rates in Clayhall and Anglesey almost doubled with an increase of 97 per cent in the period, while Elson reported 68 per cent more cases and Rowner seeing an increase of 38 per cent.
However, Alverstoke and Privett saw a decrease of 15 per cent in Covid rates, while Bridgemary North reported 11 per cent fewer cases during the period.
In Havant borough, South Hayling has seen a 100 per cent increase in Covid rates, while Purbrook and Widley have reported an 85 per cent jump in cases.
Coronavirus rates in Cowplain East have risen by 75 per cent in this period, and by 50 per cent in West Leigh.
Hayling West and North have reported 41 per cent fewer cases.