Sheffield has been upgraded to an 'area of concern' by the government after a rise in coronavirus cases, particularly in younger people.
The city's public health team says the average age of people who test positive has dropped to 35.
But the council's Director Public Health Greg Fell says people should only book a test if they have symptoms as the NHS system is reaching capacity.
In a statement Mr Fell said: ''If you are unwell and experiencing Covid-19 symptoms you need to get a test. If the booking system is not allowing you to book at the time you call please try again later.
It is important that you remain in your home and isolate to protect other people, including those you live with.''