Up to 100,000 Covid-19 tests per day could be needed as part of a widespread testing and tracking strategy as the country emerges from lockdown, a Government scientific adviser has said.

Professor Peter Horby, chairman of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), which is advising ministers, said the Government’s plans to move into tracking and tracing future coronavirus patients would be a “real logistical challenge”.

He told BBC Radio 4’s Today programme: “The test and trace capabilities are really going to be critical as we come out of lockdown.

“We will have to be able to test all those people (declaring via apps that they are displaying symptoms) and it is really a matter of scale and speed.

“One issue is how many tests we need, and if we are looking at 1,000 to 5,000 new cases per day of people with symptoms, of which maybe 5%-25% may have Covid, then you are talking about 25,000 to 100,000 tests per day.

“It is a real logistical challenge. But there is also the issue of speed as well.

“It is not much use getting the results five days later – you need it quickly so you can take the appropriate action and advise people to stay at home and also their contacts to stay at home to reduce transmission.”

He said such a testing and tracking strategy – also known as testing and contact tracing – would rely on the numbers of new cases being driven down.

Health Secretary Matt Hancock has said it is only by driving down the number of new cases that widespread testing and contact tracing will be effective.

It comes as the British Medical Association (BMA) said NHS staff need greater access to tests after slots offered to key workers ran out for the third day in a row on Sunday.

More than 10 million essential workers and their households are now eligible for Covid-19 checks as officials race to hit their 100,000-a-day testing target.

But as of 10am on Sunday, home testing kits for England were listed as “unavailable” on the Government’s website – two hours after booking slots reopened.

Following its launch on Friday, slots for both home-testing and drive-through centres in England have been used up within the first few hours.

Drive-through tests in Scotland were the only option currently still available on Sunday evening.

Dr Chaand Nagpaul, chairman of the British Medical Association (BMA) council, said the online booking system “offered no practical help” to healthcare workers.

“There is no point putting forward a proposal unless its matched with adequate capacity,” he told the PA news agency.

“What we found in the first two days was that within an hour the bookings had all been taken up, and therefore offered no practical help for large numbers of healthcare staff, who found the website had effectively closed to bookings.

“If the Government wants healthcare workers to have access to the test, it has to be in the context or providing adequate capacity, not a ‘first come, first served’ and closing within an hour.”

He added: “That’s not delivering on the needs of our health and care staff.”

Dr Nagpaul said the current testing capacity is “well, well short” of the number of healthcare staff who are currently self-isolating, as he called on the Government to go further than the target.

“Our estimate is that there are about 90,000 health and care staff self-isolating based upon the Government figures of absence rates,” he told PA.

“With that in mind, if they all wanted to have a test, clearly capacity has to match that number on that assumption.”

The Department of Health and Social Care (DHSC) said patients and health and social care workers had been prioritised for tests from the beginning of the testing regime and would continue to be.

Under the expansion of the testing, NHS and social care staff, police officers, teachers, social workers, undertakers, journalists and those who work in supermarkets and food production are among those now eligible.

Test booking slots or home testing kits will become available from 8am each day, the DHSC has said, with their release staggered throughout the day.

The Government is “working hard” to increase the availability of Covid-19 tests through the online service, according to a DHSC spokeswoman.

“There has been significant demand for booking tests,” the spokeswoman added.