People in the county say they have been asked to travel to Oldham in Greater Manchester, while others have been directed to Leicester and Builth Wells – despite there being a testing site in Ironbridge.
The Government website, used to book Covid-19 tests, has also been telling people that there are no walk-through test sites or home test kits available.
It comes as Telford & Wrekin Council has revealed plans are being made to open new ‘walk-in’ testing centres to increase capacity and make it easier for people who don’t have a car.
There is currently one testing site located in Telford and Wrekin at the Ironbridge Park and Ride car park, but it is only accessible to those who can drive.
A number of sites are being considered for the walk-in centres and there may be potential for people to turn up and get tested on the day without an appointment.
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The current issues with booking a test have been described as "really concerning" by Telford & Wrekin Council leader Shaun Davies, who says residents in the borough have told him they have been asked to travel to Chester, Newtown and Oldham when trying to book a test.
He said: " Telford & Wrekin Council worked hard to secure the drive-thru testing facility at the park and ride so our residents would have access to a test locally.
"I've had three direct approaches and they were all told Ironbridge wasn't available to them. They were told to go to Chester, Newtown or Oldham.
"That's a big journey to do, let alone if you are feeling ill.
"A lot of residents are saying if you drive past that park and ride it isn't full. There's a couple of cars.
"From social media, it seems to be a Midlands-wide thing. It's just ridiculous.
"People are rightly concerned. They are trying to get a test and do the right thing."
People have also taken to Twitter to vent their frustration over the issue.
Ironbridge Gorge councillor Carolyn Healy said: "The Ironbridge site is underused.
"I’ve been past several times and there is no one there apart from staff.
"For whatever reason the booking system isn’t sending people to the site despite there being capacity. Another mutant algorithm?"
Heloise Rees wrote: "I was told at first to go to Powys, then Aberystwyth, after hours trying phone and website I got Wolverhampton - but not Ironbridge??? which my mum drove past while I was at Wolverhampton and said was empty? I work in a school - this is only going to get worse!"
Councillor Thomas Janke, who represents Newport South and East, added: "Had similar issues on Sunday prior to 08:30. Saying nearest available was Leicester.
"However, after 08:30 it appeared that new appts were released and I was able to get tested at 09:00 that morning and my colleague at 14:00 that afternoon."
The Department of Health and Social Care says hundreds of thousands of people are being tested every day and new booking slots and home testing kits are being made available daily.
A spokesperson for the Government department said: “There is a high demand for tests and to help stop the spread of the virus we are targeting testing capacity at the areas that need it most, including those where there is an outbreak, as well as prioritising at-risk groups.
“We have the capacity to test for coronavirus at an unprecedented scale.
"We are expanding capacity to 500,000 tests a day by the end of October, increasing the number of testing sites and bringing in new technology to process results faster.”
Booking slots are made available the evening before for morning appointments, and on the morning for afternoon appointments.
The Government says, for home testing, when there is high demand it pauses the booking portal for short periods and improvements are being made to the system to ensure the distance limit does not go beyond 75 miles.
Telford & Wrekin Council says the process for booking a coronavirus test at one of the new walk-in centres will be the same as that for the current drive-in test centre; via the NHS website www.nhs.uk/coronavirus or calling 119.
Councillor Andy Burford, the council's cabinet member for health and social care, said information on their locations will be made available in due course.
He added: “We are looking to set up as many testing centres we can in places that people can reach on foot.
“The more testing sites we have in communities, the easier it will be for people who need a test, to be able to get it quickly."