A handwritten sign on cardboard informed them: “Test centre closed. Please rebook.”
In recent days testing centres all over the UK have come under strain.
In Newtown, the UK Government testing centre based at the Hafren car park near the college, closed early on Sunday afternoon.
People who arrived having booked testing slots from 4pm to 4.30pm – who included some who had travelled from Liverpool, Telford and Lichfield – were told to re-book their appointments.
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Councillor David Selby, who is also Newtown’s mayor, said: “Closing early on any day is not acceptable.”
He said he understood that the problem was the lack of capacity to process the tests, which means that testing sites are closed once a daily limit is reached.
“This is appalling and unacceptable and needs action,” he said.
“Handwritten signs are not good enough and no-one who is potentially ill should be expected to travel many miles for a test that may not even happen.”
Councillor Joy Jones, said: “Why are people from towns outside of Powys coming here?
“This could potentially spread the virus. I am sure with the best will in the world they wouldn’t mean to, but after a long journey people will possible need the toilet, drink or food, or even just stretch their legs.”
A spokesman for the UK Government Department of Health and Social Care, said: “It is disappointing to hear of people having poor experiences accessing testing.
“Over 17 million tests have been delivered so far and we are aiming to grow capacity to 500,000 tests per day by the end of October.”
The spokesman added that 90 per cent of people get a test within approximately 22 miles of where they live and for the vast majority of those it is under 10 miles.
A spokesman for Powys Teaching Health Board (PTHB), said: “We are aware of a number of issues affecting the UK Government’s Covid-19 antigen testing programme which includes the drive-through testing centres in Powys.
“We have escalated these issues to Welsh Government so that they can raise this with UK Government.”