Data from the Department for Health and Social care shows 940 people who tested positive for Covid-19 in Shropshire, and 477 in Telford, were transferred to the test and trace service between May 28 and October 7.
The service asked the patients to give details of anyone they had been in close contact within the 48 hours before their symptoms started.
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In Shropshire, 1,970 close contacts were identified – but just 63.1 per cent were reached by contact tracers over the period, meaning 727 people were not contacted or did not respond.
Meanwhile, in Telford and Wrekin, 1,127 close contacts were identified, but only 61 per cent were reached.
Shadow health minister Justin Madders said the heavily-criticised system was "falling apart", as he echoed calls for a circuit-breaker lockdown amid another surge in positive cases.
Mr Madders said: "It is absolutely staggering that week upon week the performance of test and trace keeps getting worse and worse.
"Surely ministers must see that the system is falling apart and what was supposed to be world beating is in fact now one of the biggest obstacles to us getting on top of the virus.
"The need for a circuit break is absolutely critical now and that time should be used to fix test and trace once and for all."
In Shropshire, 220 new cases were transferred to test and trace in the latest week, NHS figures show. The figure for Telford and Wrekin was 123.
Health Secretary Matt Hancock defended the test and trace system, telling MPs that it has allowed for a "detailed picture" of where and how the virus is spreading.
“This week’s statistics show the testing capacity is up, testing turnaround times are down, and the distance travelled for tests is down too," he added.
But Saffron Cordery, deputy chief executive of NHS Providers, which represents trust leaders, said: "It’s deeply unfortunate that at this point with infections rising, admissions increasing and winter looming, there’s still clearly a long way to go until our test and trace system is fit for purpose."
The Scientific Advisory Group for Emergencies (Sage) says not enough tests are being carried out, the results are taking too long to come back and not enough people are adhering to the isolation rules.
One problem is that while testing capacity has increased, this has not always reflected localised outbreaks.
Numerous reports emerged last month of people being asked to drive excessive distances for a test.
Steve Hyndside, from Stroud, was on holiday in Wales when his two children were taken ill.
He was directed to the test centre at Jiggers Bank, Ironbridge, but after a two-hour journey he was told the centre had run out of tests.
On one occasion the site was closed by police due to traffic queues and general chaos.
Telford MP Lucy Allan said a computer error caused the centre to be overwhelmed by people from across the country.
Latest figures suggest this problem has largely been resolved, with patients travelling an average of 3.3 miles for a test.
But questions are also being asked about testing capacity itself.
Prime Minister Boris Johnson pledged 500,000 tests a day by the end of the month, but this looks ambitious.
The most recent figure, for the week ending October 7, showed capacity at just 309,000.
This was a five per cent increase on the previous week, but the figure will need to increase by nearly15 per cent a week to meet the target.
On the positive side, four new laboratories are due to open in the coming weeks.
The new labs are also needed to shorten the time taken to deliver test results.
Sage says tests need to be returned within 24 hours by start of the winter flu season.
While the latest figure show some improvement, just 68 per cent of in-person tests are returned the next day.
Management of test data has been another problem.
Last month nearly 16,000 coronavirus cases went unreported because of a computer error, and the Government's first attempt to create a mobile-phone app to track infections was abandoned in June.
Earlier this month, the NHS introduced a new phone app.
All eyes will be on whether this, and the increased testing capacity, will finally get to grips with tracking the virus.