Liz Noakes, director for public health at Telford & Wrekin Council, was speaking as the borough confirmed the number of cases over the seven days up until Sunday was 22 – slightly down on the 26 the previous week.
She said that although the number of cases is similar to the previous week, when the total for the last month is compared to the previous month there has been a notable increase.
Ms Noakes said that the increase made it all the more important that people follow government guidance on social distancing, hand washing, wearing of masks, and other measures.
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She said: "We have got cases emerging in older and more vulnerable residents. It is about protecting those people, that is why it is important that we all follow the rules. It is the same message, and it is about protecting those people."
The message comes as several parts of the West Midlands have been put into government imposed lockdown, or self imposed restrictions.
Ms Noakes said the increasing number of cases was also evident in hospitals, with admissions rising.
She said: "Hospital admissions in the West Midlands conurbation are going up and for those most at-risk this is still an incredibly serious infection."
Ms Noakes also said there was a concern about the increase across the West Midlands, with the natural ties between Telford and the area making it vital that guidelines are followed.
She said: "It is a cause of concern and clearly we can have residents here that work in the West Midlands, but we can also have it the other way round in terms of people coming from the West Midlands to the borough."
There has been much concern over access to testing in the county, as well as across the UK, and the director said that improvements are needed – both in care home testing and at public centres such as the one at Ironbridge.
The situation with the permanent testing site at Ironbridge has generated considerable frustration – with the council and Telford MP Lucy Allan raising the situation with the Health Secretary.
There have been repeated complaints from local residents unable to access a test, who have found they have been diverted to Mid Wales, Oldham, and even Scotland, in search of an appointment.
The situation descended into farce at one point with people from outside the county being directed to the centre, causing huge queues and its early closure.
The problem with testing is understood to be the number of actual test kits available, and the laboratory capacity for processing tests.
The government has said this will increase in coming weeks with the addition of extra laboratories.
Ms Noakes said the speed at which results are being returned to care homes is "not good enough", and neither was the situation with access to testing appointments for the public.
She said: "In care homes the staff are being tested once weekly and the residents once a month.
"The time it is taking to get results is not good enough. The whole point of testing is you are getting the results back in a timely manner so if you have the infection you can isolate and you can take the right action."
She added: "I think the it is also not good enough that people with symptoms are not able to get easy access to testing and get timely results. The situation last week, that has continued and it is not good enough."
Ms Noakes said that when people were unable to access appointments through the government website they should keep trying, as slots do become available, sometimes an hour or so later.