More than one in four people who test positive cannot be reached by the test and trace system in England, data shows.
In the first two weeks of operation to 10 June, the service was given the details of 14,000 people to follow up.
But fewer than 10,200 could be reached. Some failed to provide the right contact details, while others did not return calls.
The service has asked over 87,000 of their close contacts to self-isolate.
That represents nine in 10 of the people whose details they were given by those who were infected.
What is not clear – because the government is not publishing these figures – is how quickly close contacts are being reached after the positive case is tested.
To be most effective, this should be done within 48 hours of the test being carried out.
Prof Keith Neal, an expert in controlling infectious diseases at the University of Nottingham, said the results were “very encouraging”, although he described it as worrying that more than a quarter of people could not be reached.
“This is a public health crisis – the public are key to helping stop it.”
He also played down concerns that the tracing app might not be available for months, describing it as the “cherry on the cake”.
He said it had a role in identifying close contacts in situations where you did not know the individuals, for example people you were close to in a shop or on public transport, but these would be at “low risk” anyway.
Ministers have said the public has a “civic duty” to engage with the test and trace system.
Dido Harding, head of England’s test and trace system, said it was “undoubtedly helping to save lives”.
“We continue to rely on everyone to play their part, and we urge those with symptoms to book a test immediately, and those contacted by the test and trace service to follow the advice they receive.”
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