Professor Helen Stokes-Lampard, a Lichfield GP and chairwoman of the Academy of Medical Royal Colleges, said five members of staff at Westgate Medical Practice could not come into work at the start of the week.
Professor Stokes-Lampard said: "The current testing debacle is intensely frustrating for all healthcare professionals.
"We currently test more per capita then almost any country in Europe, and it's growing, but what seems to have gone wrong is that over the summer when coronavirus had dropped away there was very little demand for testing and the laboratories were sitting idle.
"The advice was if in doubt get tested, as the socialising of the summer has happened and people have been encouraged to build back the economy, go to work and children have mingled, we've had a surge in all the normal viruses.
"We've had lots of kids with low grade temperatures and a cough which means they need to be tested.
"There's evidence of a lot of people requesting testing just in case which was fine a few weeks ago but we now need to be enforcing the rules about who should be tested."
She added: "In my own practice at the start of the week we had two doctors and three administrative members unavailable to come to work.
"That's five staff out of 100 unavailable to be in work because they were at home trying to get themselves or a family member tested or awaiting results.
"We've got countless examples of people being offered tests in South Wales and in the north.
"People spend hours trying to book a test, there are issues."
It comes after ministers have been urged to get a grip on coronavirus testing in the region as the system was plunged further into chaos.
Across the Black Country and Staffordshire people with Covid symptoms are struggling to get pre-booked tests at local centres – while some have been told they need to travel more than 400 miles to Aberdeen for a test.
Hundreds have been turned away from centres which have hit full capacity, with some walk-in test centres now switching to an appointment system after struggling to cope with demand.
In other areas people are being turned away even though there appears to be little activity.