In the last two weeks, coronavirus cases in the wards of Edgmond & Ercall Magna and Donnington have been high, and despite testing rates being low, a large proportion are showing positive results.
Telford & Wrekin Council is urging residents in those locations to get tested if they have any of the main coronavirus symptoms, or show no symptoms but leave the house regularly for essential purposes such as work.
People should self-isolate immediately and book a test if they show any signs of Covid-19, including a high temperature, a new, continuous cough or a loss or change in sense of smell or taste.
A free NHS test can be booked on the government website.
Residents do not need to self-isolate but are being advised by the council to get tested as a precaution if they show any additional symptoms such as headaches, aches and pains, feeling very tired for no good reason, sore throat, runny nose, sneezing and nausea in children.
Telford & Wrekin Council said many people showing precautionary symptoms test positive for Covid-19.
Those booking a test can select "My local council or health protection team has asked me (or someone I live with) to get a test, even though I do not have symptoms" when doing so via the government website.