Greg Fell, the director for Public Health Sheffield, hit out after No 10 suggested more restrictions could be lifted on 1 June – including schools reopening – even if the programme is hit by further delays.
“I think we need to have the test and trace system working before we start to fundamentally reopen society,” Mr Fell said.
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“To not do so gives the virus unchecked opportunities to spread and that will lead us back to a place that we have been before – and nobody wants to go back there.”
The warning comes after Matt Hancock refused to set a date for test-and-trace starting – after the mid-May target was dumped – despite announcing 21,000 tracers had been recruited.
Thérèse Coffey, the work and pensions secretary, sparked further confusion when she said the troubled smartphone app – still being trialled in the Isle of Wight – had to be operating before physical tracing could begin.
It has been held up by problems over compatibility with some phones, by concerns that it drains phone batteries and hints the government may yet switch systems and start again.
Mr Hancock has carried out a quiet U-turn by recruiting 7,500 medics as part of his 21,000-strong army, after criticism that having only 3,000 was doomed to fail.
However, the majority will still be lowly-paid call handlers, recruited by private firms including Serco, and given as little as one day’s training.
Speaking to BBC Radio 4’s Today programme, Mr Fell urged ministers to recognise that test-and-trace is “fundamental to breaking chains of transmission and reopening society”.
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He admitted even he did not “know the final details of how it will work” – despite being a public health chief in one the country’s biggest cities – but said trained staff had to do the “heavy lifting work”.
Mr Fell pointed to the difficult work of contact tracing in tightly-knit communities, or a special school or care home, adding: “That can’t be managed only by people working in a call centre 250 miles away.”
Both test-and-trace and use of the smartphone app have been put back until “the coming weeks”, even though phase two of restriction-easing is due to start on 1 June.
Boris Johnson’s spokesman insisted phase two would not be delayed even if testing and tracing was not ready – insisting there was no “explicit” link.