Testing for coronavirus will be ramped up amid criticism that NHS staff are being lost from the frontline over potentially harmless coughs, while private clinics report being “inundated” by people who can afford to pay for swab checks.

The Scottish Government says some Covid-19 testing on healthcare workers has already started at a local level and a national approach is being developed which will scale up these initial efforts.

It comes amid speculation that a new four-hour test could be made available in Britain.

Scotland reported its third coronavirus death on Wednesday and First Minister Nicola Sturgeon confirmed schools across Scotland would close by the end of this week as a result of “new advice” from Government scientists.

They will also close in England, Wales and Northern Ireland.

Ms Sturgeon said many schools had reached a point where “they have lost too many staff to continue as normal” and would not necessarily reopen after Easter, or even before the summer holidays.

Prime Minister Boris Johnson said schools and nurseries across the UK would be expected to accommodate vulnerable children or the children of critical workers, such as NHS staff and police during the closure, with free school meals continuing to be provided to all eligible youngsters.

He added that exams would not go ahead as planned in May or June, but that pupils would “get the qualifications they deserve”.

Earlier Mr Johnson told the House of Commons the number of tests that can be carried out each day for coronavirus will be increased from 5,000 to 10,000, with a goal to expand it to 25,000 per day in England within four weeks.

North of the Border, there are three NHS laboratories currently processing tests and the Scottish Government is working with a range of partners to increase capacity to exceed 2,000 tests per day in the coming weeks.

A number of options to expand that further, and as quickly as possible, are being explored.

The Prime Minister said: “We are prioritising testing of NHS staff for the obvious reason that we want them to be able to look after everybody else with confidence that they’re not transmitting the disease, and this country is actually far ahead of many other comparable countries in testing huge numbers of people.”

It comes as a coronavirus test that reveals who has had Covid-19 but not shown symptoms is close to becoming available in a move being hailed as a “game-changer”.

The Government’s chief scientific adviser, Sir Patrick Vallance, said Public Health England’s (PHE) work on the antibody test is “progressing very fast”, and will provide valuable insight into the pandemic.

Mr Johnson said: “The great thing about having a test to see whether you’ve had it… is suddenly a green light goes on above your head and you can go back to work safe and confident in the knowledge that you are most unlikely to get it again.

“So for an economic point of view, from a social point of view, it really could be a game-changer.

“You can really see the potential of that advance, which, as I say, is coming down the track.”

Sir Patrick added: “It is a gamechanger. And the reason it’s a gamechanger is that it allows you to understand the proportion of the asymptomatic population – who’s had this disease, but hasn’t had symptoms.

“Going forward it’s going to be critically important to be able to monitor this disease well because only by being able to monitor it can we start relaxing measures again.”

The Scottish Government is increasing community surveillance by enabling 200 GP practices, representing a population of 1.2 million, to test patients for the virus.

Health Secretary Jeane Freeman has also promised to roll out testing to frontline NHS staff “so that they do not self-isolate unnecessarily”.

However, there has been criticism from medics that the process has been too slow and has left key services understaffed at a time when demand is soaring.

Glasgow GP Margaret McCartney tweeted: “Our workload has increased 30-40 per cent in last two days.

“I know everyone is very busy but a negative test in a symptomatic person would surely allow us to have a hope of functioning?”

British Medical Association Scotland chairman Dr Lewis Morrison said: “The impact Covid-19 will have on the NHS could be huge. Frontline workers will be working in very different ways and we will need every pair of hands we can possibly get at this time.

“That is why it is essential for NHS staff to be tested for the virus if they suspect they have it.

“The Scottish Government has assured us this will happen and we now need to see the details of how staff can access testing as soon as possible, to minimise the number of NHS staff who would otherwise be self-isolating.”

Professor Michael Griffin, president of the Royal College of Surgeons Edinburgh, said: “The recommendation from the UK Government on Monday that pregnant women should self-isolate, as well as a 14-day isolation of those who have been exposed to family members with symptoms, though understandable, has already put a huge pressure on the NHS workforce.

“That’s why it’s absolutely imperative that healthcare workers are tested for Covid-19 – to confirm whether they are infected – in order to help prevent the unnecessary exclusion of essential NHS staff at the frontline when the epidemic hits its peak.”

A test is available for £375 at the Private Harley Street Clinic in London.

Mark Ali, a doctor at the clinic, said it had been “inundated” with requests for the test, which can be couriered to and from a client for them to take swabs from their own nose and throat.

Mr Ali said: “We are testing lords and ladies, knights, and even doctors and dentists who are worried about catching the disease.”

As of March 12, the UK had tested just under 30,000 people – more than any other European nation except Italy, which had tested 86,000 and Russia which had tested 80,000.

The US had tested fewer than 14,000 in official Centre for Disease Control (CDC) laboratories, compared to 250,000 in South Korea.

Scotland has carried out 6,091 tests to date. US firm ThermoFisher held talks this week with the Prime Minister, Health Secretary Matt Hancock, Chief Medical Officer Chris Whitty, Chief Scientific Advisor Sir Patrick Vallance and representatives from Boots, Amazon and pharmaceutical giant Roche.

The firm is believed to have been demonstrating its four-hour testing kit which has been approved for use in the US.

The UK death toll from the virus has reached 104 – exceeding 100 for the first time – and the number of new cases is accelerating, with 676 new cases confirmed yesterday.

Organisers announced that the Glastonbury music festival and Eurovision Song Contest would not go ahead due to the coronavirus outbreak, with filming also suspended temporarily on BBC soaps including Eastenders and Casualty.

It comes as China’s top coronavirus expert has warned that “herd immunity” will not contain the global pandemic because the disease is highly infectious and lethal.

Dr Zhong Nanshan, China’s senior medical adviser, said: “We don’t yet have the evidence to prove that if you are infected once, you would be immune for life.”

Clinical trials for potential vaccines are under way in China and the US, but is not expected to be ready until at least 2021.

Meanwhile, an antiviral drug used in Japan to treat influenza has shown potential to speed recovery from the novel coronavirus that causes Covid-19. The drug, called called Favipiravir or Avigan, was tested on 340 people in China who had been diagnosed with Covid-19.

Half tested negative for the virus within four days of being given the drug compared to 11 days for the patients not on the antiviral.

Lung conditions were also shown in X-rays to have improved in 91 per cent of participants.

There were also claims in China that patients could be cured using stem cell therapy.

Dr Dongcheng Wu, a doctor and stem cell expert based in Wuhan, the epicentre of the outbreak, said he had successfully treated nine patients who were hospitalised with novel coronavirus pneumonia.

All nine reportedly made a full recovery following stem cell transplants and conventional treatment. Dr Wu said: “Yes, it is a cure but it is still very early in the process.”

It came as Italy recorded 475 coronavirus deaths in a single day – the highest 24-hour spike for any country since the infection emerged in China.