Shropshire Council's director of public health, Rachel Robinson, said there are currently a total of 74 Covid outbreaks being handled by the authority – with 36 new ones in the seven days up to September 16.
She said that most of the outbreaks were in schools.
The overall rate of cases in Shropshire has fallen to 308.5 per 100,000, although the neighbouring area of Telford & Wrekin currently has the eighth highest rate in the country – 405 cases per 100,000 people.
Telford & Wrekin saw 734 cases reported in the seven days up to September 19, according to the council's latest update, while Shropshire had 1,004 in the week up to September 16.
The number of non-vaccinated people in Telford & Wrekin also remains nearly 30,000, prompting renewed pleas for people to get the jab.
Councillor Andy Burford, the council's Cabinet Member for Health and Social Care, said: "There are still around 29,370 people in our borough who are eligible for vaccines now. Please do book an appointment to receive your first dose.
"If you have any vaccination concerns, please speak with your GP or with the clinicians at a walk-in clinic.
"Several Covid-19 walk-in vaccination clinics continue to be available across the borough – no appointment needed. Or you can book your vaccination slot on the NHS website."
Meanwhile Dean Carroll, Shropshire Council’s Cabinet member for public health, said it appeared some people were beginning to stop following guidance regarding Covid.
He said: "We know many people across Shropshire have and continue to follow the national guidelines by getting vaccinated and regularly tested, wearing masks in crowded spaces, letting fresh air in when indoors and social distancing.
“However, we’re also seeing people disengaging with such advice. I can’t emphasise enough that all us need to take personal responsibility, not just for our safety but the safety of our loved ones, friends and our wider community.
“We are having to live with Coronavirus and while restrictions have relaxed, I urge everyone to continue to follow these guidelines, otherwise we will continue to see cases rise across Shropshire.”
Mr Robinson said there had been an increase in Covid patients at county hospitals – most of which had not been vaccinated.
She said: "While there was a slight decrease in numbers of cases last week, with the number of outbreaks in schools and the wider community continuing to rise, we are now seeing figures increase again. Our health protection team is currently managing 74 Covid-19 outbreaks, mainly across schools, with 36 new outbreaks declared in the last week.
“Sadly, we’ve seen a further five deaths in our hospitals, who continue to see an increase in hospitalisations of Covid-19 patients, the majority of which remain unvaccinated, which is concerning.
“I would therefore urge anyone who has not yet had their vaccine to please take up the offer. The NHS ‘evergreen’ vaccination offer is for anyone who has yet to accept the opportunity to be vaccinated. You can still get your first and second doses at walk-in clinics across the county.
“Not only will this help stop the spread of the virus but also help reduce the risk of serious illness.”