Scientists have warned it is essential to quickly identify the “index cases” – those who test positive for the virus – in order to then trace their contacts before the infection spreads any further.

In an update to industry figures on July 9, Mr Cooper said: “Essentially where we sit with test and trace at the moment is we are identifying around a third of the people we really should be finding. So the main challenge for us now is to make sure that we can test more and identify those index cases.

“It depends on which modelling you get, but we need to be finding roughly half of the people that have got Covid-19 so that we can keep R down, if test and trace is going to work. So the challenge for the service over the next few weeks is to drive that 37 per cent up to 50 per cent.”

Mr Cooper said Test and Trace could increase the figure by ensuring that a greater proportion of people with symptoms take a test, and by offering tests to asymptomatic workers in “high risk groups”, such as taxi drivers and staff at food processing plants.

“We’re going to be running out that part of the programme over the next couple of weeks,” he said. Asked how testing would be used to help reopen schools and universities, Mr Cooper revealed that officials were examining the possibility of making testing units “available on university campuses”.

On Saturday, Prof John Edmunds, a member of the Government’s Sage advisory group, said: “The big risk is September where the schools will have to return, and colleges and universities, which obviously millions of people attend.”

Meanwhile, those using swab tests at home and posting them to a lab were waiting an average of 70 hours last month – a figure that has since been halved.

“You can do a test in your own home, you can drop it into a post box, and you’ll get a result. At the moment the median time is 35 hours,” Mr Cooper said. “That was about 70 hours five weeks ago.”

A Department of Health spokesman said: “NHS Test and Trace has already helped test and isolate more than 180,000 cases – helping us control the spread of the virus, prevent a second wave and save lives.

“We are also carrying out asymptomatic testing of some key workers – taxi drivers, cleaners and retail assistants – as well as people in areas with local outbreaks, to identify those who have the virus but don’t show symptoms.

“These efforts mean more people know to self-isolate, stopping the virus spreading further.

“We urge you to book a test if you have symptoms, self-isolate and help us trace anyone you’ve been in contact with.”

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