Councillor Andy Burford, Telford & Wrekin Council's cabinet member for health, has also spoken of concern at the rapid rise in infection rates in the over 60s.
For the week ending November 8 there were 600 new cases in the borough, an increase of 157 from the week before.
The seven day infection rate for Telford and Wrekin is 334 confirmed cases of Covid-19 per 100,000 of the population – above the West Midlands average of 326, and the England average of 254.
There are also currently 47 people diagnosed with Covid-19 in either Royal Shrewsbury Hospital or Princess Royal Hospital Telford.
Councillor Burford said: “It is deeply concerning that the infection rates among over 60s population in Telford and Wrekin has risen so sharply.
“We need to make the most of this four week lockdown to prevent the spread of the virus, particularly to older more vulnerable members of our family and community.
“Please stay home, only leave home for food, medical reasons, exercise, education, and work from home if you can."
There is significant concern over the number of cases in the over 60s, with the infection rate increasing by 91 per cent on the previous week to 272 per 100,000.
Liz Noakes, Telford and Wrekin Council’s Director of Public Health, urged people to take action to reduce the risk of people becoming seriously ill.
She said: “It is well known that the older you are the great the risk you are from Coronavirus, so we need to do all we can to protect older family members.
“If the rates of infection in the over 60s continues to rise then we can expect more people to be admitted to hospital putting a strain on local NHS resources, and sadly more deaths.
“We know that this virus spreads primarily through families and social contact, during this second lockdown we need to be doing all we can to stay at home and to limit contact with others.
“To prevent people from passing on the virus it is imperative that people immediately self-isolate and get tested as soon as you have any of the three key coronavirus symptoms, however mild.
“It has never been easier to get a test, with seven sites in the borough that people can drive or walk to get tested and plenty of capacity, you should be able to get a slot on the same day you book.
“You can book a test 24/7 online at nhs.uk/coronavirus or by calling 119.”