NHS Test and Trace is still reaching fewer than half of close contacts as experts say this is not enough to prevent a second wave.
The Government has been accused of “misrepresenting” the data as analysis for the Mirror showed just 45% of contacts were being reached by call centre staff at the end of August.
It follows modelling published in the Lancet journal showing this must be at least 68% by the time schools went back.
Despite this, Health Secretary Matt Hancock on Thursday claimed the system was “working well” after Boris Johnson had repeatedly claimed it was “world beating”.
The latest tranche of testing data for the week ending August 26 shows of those close contacts provided by people who recorded a positive test, only 69% were reached.
This was down from 77% the previous week.
Prof Chris Bonell, author of the Lancet paper, calculated the percentage of contacts reached, minus those who initially recorded a positive test but could not be reached or who did not provide recent contact details.
It found that overall just 45% of overall contacts were reached, down from 51% in mid-July.
Prof Bonell, of the London School of Hygiene and Tropical Medicine, told the Mirror: “The rate of contacts being reached has actually gone down.
“The overall 45.3% figure is nowhere near the 80% level of coverage that SAGE previously suggested as a target or the 68% figure that our model suggested was needed to prevent a second wave.
“Rather than using statistics selectively to misrepresent our tracing system as ‘world beating’ we need to take radical steps to improve it.”
Yesterday’s rate is only a small improvement on the first week of the programme when 40% of close contacts were reached.
The modelling by the LSHTM and University College London found this needed to be 68% once schools go back.
The Government has repeatedly insisted the system was rapidly improving.
Minutes of a Sage meeting on May 1 stated: “Sage discussed the test and trace system in development.
“It agreed that at least 80% of contacts of an index case would need to be contacted for a system to be effective.”
Mr Hancock has previously used some dubious maths to claim this target had been hit.
When looking at only those contacts where details had been obtained from the person to record the initial positive test, the Government calculated that 80% of these contacts had been reached.
Prof Bonell and other experts are demanding follow-up calls to record how many people asked to self-isolate actually do so.
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Prof Sheila Bird, biostatistician at Cambridge University, said: “British science can and should do infection control better than NHS Test and Trace is delivering.”
Prof James Naismith, of Oxford University, said: “The test and trace system appears to be showing some strain.
“Many scientists cautioned that the challenges that setting up a test and track system from scratch in such a short time were being underestimated by politicians.”
Justin Madders, shadow health minister, described the latest figures as “hugely disappointing” and said there was “clearly a problem with testing infrastructure”.
He said: “With cases on the increase and the Government pushing for everyone to return to work, it is more important than ever that test and trace is working to its potential.”
A Government spokesman said: “NHS Test and Trace is working. Hundreds of thousands of people are being tested every day and the service continues to reach the majority of those testing positive and their contacts, reaching 80% of contacts where contact information was available.”
One reason for hope came in the form of a £50 million trial of rapid turn around spit tests in Southampton and Trafford in Greater Manchester.
The 20-minte tests has been found to be “almost as good” as the standard PCR swab test, so suitable for mass testing.
It could be further expanded in the coming months.
Mr Hancock said regular mass coronavirus testing on schoolchildren, shoppers and commuters could be key to having a normal Christmas.
He said: “Short of a vaccine this is the best chance we have of reducing social distancing and controlling the virus, especially with winter coming.
“I hope that if this mass testing regime comes off, if the new technologies we’re working so hard on work, or if we manage to get a vaccine before now and then, then I hope we can have a happy and loving Christmas that people yearn for.”