Data has shown just over 50 per cent were contacted and told to self-isolate in the Black Country and Staffordshire, because the system had found they had come into contact with Covid-19.
Data from the Department for Health and Social care shows 1,302 who tested positive for Covid-19 in Wolverhampton were transferred to the test and trace service between May 28 and October 7.
The service asks these patients to give details for anyone they were in close contact with in the 48 hours before their symptoms started.
In Wolverhampton, 2,893 close contacts were identified – but just 56.2 per cent were reached over the period.
In Dudley, 1,043 who tested positive were transferred to the test and trace service in the same time, with 2,534 close contacts identified.
But just 62.8 per cent were reached by contact tracers over the period, meaning 942 people were not contacted or did not respond.
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Over in Sandwell, 2,377 who tested positive with 5,385 close contacts discovered, but just 56.4 per cent were reached by contact tracers.
A total of 1,427 tested positive for Covid-19 in Walsall during the same time, and 2,817 contacts were identified.
However, just 62 per cent were reached by tracers over the period, meaning 1,071 people were not contacted or did not respond.
Elsewhere, in Staffordshire, 3,012 who tested positive for Covid-19 were transferred between May 28 and October 7.
A total of 6,573 close contacts were identified, with 64.5 per cent reached by over the period.
The data has shown the numbers are dropping further, according to figures in the latest week until October 7.
The weeks previous had shown slightly more were being contacted through the system, but these numbers have now gone down.
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 Wolverhampton, 258 new cases were transferred to test and trace in the latest week, NHS figures show.
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."
When Boris Johnson announced the 'world beating' test-and-trace system in May, he said it would be crucial to restoring normality to the Covid-hit Britain.
In the absence of a vaccine, he said it would enable people to go about this business as normal, visiting friends and families, going to work, and preventing economic disaster.
Five months on, serious questions are being asked about the system as it emerged that thousands of people are slipping through the net.
And now, with lockdown measures being slowly reintroduced, and a second wave looming, the Government's own advisers are warning that the system is not working properly.
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.
The UK is not alone in experiencing problems with test and trace. France and Spain, in particular, have had similar difficulties, but other countries, such as Singapore, South Korea and Germany, appear to have fared better.
One criticism is the UK system has been too centrally controlled, without enough input from local directors of public health, who have experience of running such systems to tackle local outbreaks of food poisoning or sexually transmitted diseases.
Andy Street, the regional mayor of the West Midlands, appeared to support this argument this month when he said: “We’ve always known there was a need for a local element of test and trace, as a centralised system does not have local expertise and is not able to cut through the harder-to-reach communities."
Another problem has been that while testing capacity has increased, the tests have not always been in the right places to reflect localised outbreaks.
Numerous reports emerged last month of people being asked to drive excessive distances to get a test, including Wolverhampton councillor Milkinder Jaspal, who had to travel 412 miles to Aberdeen for a test after experiencing Covid symptoms.
There were reports of traffic queues and general chaos at the testing site at Jiggers Bank, Ironbridge, which on one occasion was closed by police.
Latest figures appear to 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.
Dido Harding, who is in charge of the test and trace system, last month said the number of people wanting tests were three to four times the number available, with the main laboratories operating at capacity levels.
Thousands of tests are said to have been sent abroad for processing.
Thousands of people are said to have been turned away from testing centres after coming into contact with somebody who tested positive, simply because they were not showing symptoms.
The Prime Minister has pledged that daily testing capacity would reach 500,000 by the end of the month, but this figure looks ambitious.
The most recent figure, for the week ending October 7, showed capacity was 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 expected to open in the coming weeks, which should alleviate the problem to some extent.
The new labs are also needed to shorten the time it is taking to deliver test results.
Sage said it was essential tests were 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.
And for tests carried out in the home, the turnaround time actually increased.
There have also been problems with the management of test data.
Last month nearly 16,000 coronavirus cases went unreported because of a computer problem, 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.