The Government has faced mounting pressure over failings in the process which has seen up to four times the number of people trying to book a test as are available across the UK.
It comes as a new tracing app is launched today in a bid to contact more people through the service if there is an outbreak.
Data from the Department for Health and Social Care showed that the 474 people who tested positive for Covid-19 in Shropshire and the 214 in the borough of Telford & Wrekin were transferred to the NHS Test and Trace service between May 28 and September 9.
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Details of a further 907 confirmed coronavirus sufferers in Shropshire – along with 530 in Telford & Wrekin – who had been in close contact with the person within 48 hours before their symptoms started, were handed over for the NHS service to contact.
The close contacts are referred to as being “non-complex” cases, which means they can be dealt with through a call centre by the service or online.
Of those close contacts, 62 per cent of people from Shropshire and 60 per cent from Telford & Wrekin were reached – meaning a combined total of 557 have not been reached.
Baroness Dido Harding, who heads up the service, said the demand for tests was outstripping capacity – but denied the claims the system was failing.
It comes amid rapidly rising case numbers, which experts suggest may result in tens of thousands of new cases every day by the middle of next month.
No figures were available for Powys.
Fears that test service 'is falling well short’
In England, only 64 per cent of non-complex contacts have been reached by the Test and Trace service, in the week up to September 9.
NHS Providers chief executive Saffron Cordery said the figure fell “well short” of the 80 per cent target set by Scientific Advisory Group for Emergencies (SAGE) which has been advising the Government.
In May SAGE said the service would need to reach at least 80 per cent to be deemed “effective”.
Ms Cordery said: “Trust leaders are increasingly concerned with the current testing shortages impacting on NHS service recovery and winter preparations due to staff and their family members being unable to access a test.
“Additionally, with the number of positive Covid-19 cases increasing, but a reduction in the proportion being contact traced, we are looking at renewed pressure on the NHS.”
A contact is deemed not not reached when there has been no response to text, email, call reminders, or when their details are not available.
Health Secretary Matt Hancock, who has has vowed to find the cause of the system glitch that saw hundreds of cars descend on a Telford coronavirus testing centre on September 8, has said the launch of the new app will help “control the spread” of the virus through “cutting-edge” technology.
He said: “The launch of the app across England and Wales is a defining moment and will aid our ability to contain the virus at a critical time.
“It is vital we are using the NHS Test and Trace system to reach as many people as possible to prevent outbreaks and stop this virus in its tracks. This function will make it simple and easy so we can keep this virus under control.”
From September 28, people in England will legally have to self-isolate for 14 days if they test positive for coronavirus, or if instructed to do so.
Fines for non-compliance will start at £1,000, rising to £10,000 for repeat offenders, while those on benefits will be eligible for a one-off support payment of £500 if they face a loss of earnings as a result of having to quarantine.