The huge stock of 17.5m antibody home testing kits ordered by the government after Boris Johnson said they could be a “game changer” could in fact be unreliable, scientists have said, saying that they may fail to detect up to half of coronavirus cases.

After the prospect of the pregnancy test-style kits was first raised, it was suggested the tests would be made available “within days” on Amazon and via Boots, to allow people who have had the virus to return to the workplace confident in the knowledge that they are safe.

But in recent days, ministers have appeared to play down the likelihood of the tests being universally effective, with the health secretary, Matt Hancock, saying on Sunday that the tests were not yet “good enough”.

Now scientists involved in validating home testing kits have told the Guardian that no test on the market has yet been shown to be sufficiently reliable. Some kits, which claim a more than 90% rate of accuracy, appear to have been tested only in hospital on patients with very significant symptoms.

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One expert told the Guardian that in reality the sensitivity of the tests was likely to be relatively low and more likely to detect 50%-60% of those with milder symptoms – the group for whom the tests were intended.

The warnings over the limit to the value of the tests came as another 621 deaths were announced, a drop on the previous day’s record total of 708.

Meanwhile on Sunday:

• Hancock criticised the “unbelievable” behaviour of people packing into parks at the weekend and said rules on exercise could change before clarifying that the government was “not planning any changes imminently”.

• Scotland’s chief medical officer, Catherine Calderwood, apologised after it emerged that she went to her second home during the lockdown and withdrew from being the public face of the government’s information campaign north of the border.

• Italy recorded its lowest number of cases in two weeks, with the total number of people in hospital with the virus falling for the first time since the beginning of the crisis.

• Sweden prepared legislation to allow it to take “extraordinary steps” to tackle the crisis, as concerns continued that its unusual “slow spread” strategy was not working.

• A nurse and a midwife who died last week in the UK were named, while the Marquess of Bath, the owner of Longleat safari park, was also announced to have died.

The scepticism over the value of the tests comes at a time of ongoing concern over whether the details of UK government pledges on coronavirus stand up to scrutiny. Last week ministers were widely criticised for fluctuating claims over the total number of tests that could be conducted each day, with Boris Johnson’s initial claim that 250,000 was possible superseded by Hancock’s promise to scale up to 100,000 a day by the end of April.

On Sunday, Hancock appeared to contradict himself over the production of the ventilators crucial to treatment of the most severe coronavirus cases, telling the BBC that there “should be another 1,500” in a week’s time before telling the Downing Street briefing “we haven’t got an exact figure”.

He had announced the purchase of 3.5m antibody test kits on 24 March but a week later it emerged that they had not been bought, but rather had “contracts agreed subject to testing”.

The big range in immune response seen across the population also raises the troubling prospect that those who have had mild symptoms may not have long-term immunity against Covid-19.

Prof Marion Koopmans, head of virology at the Erasmus University Medical Centre in Rotterdam, whose lab is assessing home testing kits in the Netherlands, said: “So far, I’m not aware of any home tests that have passed our quality mark. Based on what I’ve seen so far I’d be hesitant to give you an immunity passport based on a rapid test result.”

A senior UK scientist who is working on lab-based antibody testing for Covid-19, said that given the current state of knowledge he was “amazed the government had sufficient confidence” to go ahead with the purchase of millions of tests. “A lot of us did a double-take,” he said.

Another UK scientist said that none of the home test kits currently under evaluation in the UK were performing well enough, but did not give specific performance figures.

Last month, Boris Johnson described the kits, which take as little as 20 minutes to use, as a potential “game changer” and their use is outlined in the government’s five pillar testing strategy. However, this weekend Hancock played down expectations, telling BBC One’s The Andrew Marr Show that there were no immediate plans to roll out antibody testing kits. “We’re getting the test results through every day, I was looking at some last night,” he said. “But we still don’t have any that are good enough.”

Emerging evidence suggests that there is a wide range of antibody responses to coronavirus across the population, which may make the development of a simple, reliable home test that will work for everyone a considerable challenge.

Dr David Ho, a leading infectious disease specialist at Columbia University in New York, said that, based on patient samples analysed by his team, those with severe illness tend to develop a faster and stronger antibody response. In people with milder symptoms, the presence of antibodies in the blood tends to ramp up more slowly, meaning that tests need to performed later.

“The problem is after a couple of weeks, the detection rate remains at about 50%-60%, especially in asymptomatic or mildly symptomatic cases,” Ho said. “But this may not be a fault of the tests, because even using more sensitive methods in the lab we can see the antibody levels are quite low.”

It is not yet clear whether this 50%-60% figure will improve much if people are tested three or four weeks after infection. To answer this, recovered patients need to be tracked for a longer period, but Koopmans is not optimistic that the detection rate will reach the levels seen in severe cases.

“The sensitivity of these tests, I expect, will be relatively low,” she said. “I wouldn’t be surprised if you end up around 50%-60%. Even if they’re not that costly, why burn all those assays if that’s the information you get?”

Some of the commercial home tests claim, in promotional materials, to have sensitivities above 90%. However, these figures are likely to be based on tests in patients recovering in hospital, who represent the most severe end of the spectrum in terms of symptoms. “There’s this missing piece of how does it work in the 85% of people in the other category,” said Koopmans.

A Department of Health and Social Care spokesperson said: “Antibody tests offer the hope that people who think they have had the disease will know they are immune and get back to life as normal. We are currently working with several companies who are offering these tests and are evaluating their effectiveness.

“The Covid[-19] scientific advisory panel, led by Prof Sir John Bell, is currently undertaking a rapid evaluation process to establish their reliability. We will publish the results of this evaluation once it is completed.”