The UK government’s pledge to carry out 100,000 coronavirus tests a day by the end of the month is unravelling, with NHS laboratory staff and scientists warning they do not have the test kits, chemicals and components they need to scale up.

Boris Johnson is personally calling the major companies that make test kits to try to secure the UK supply, it has emerged, in competition with prime ministers and presidents from around the world.

NHS lab staff and biomedical scientists talk of intense frustration, saying they have the labs ready but cannot get the materials, which include test kits, reagents and plastics such as small tubes and pipettes.

“On behalf of the biomedical scientists and laboratory staff of the NHS, the Institute of Biomedical Science (IBMS) wants to express the frustration of our members and clarify that we are testing to the limit of our materials and that we are ready to increase capacity – but only if we are given what we need,” they said in a statement.

Matt Hancock, the health secretary, talked with confidence of achieving 25,000 virus tests a day for those ill in hospital and NHS staff who have symptoms or are in a household with somebody who is sick, so that they can go back to work. These are PCR (polymerase chain reaction) swab tests, sometimes called antigen tests, which need to be processed with specialised kits in a lab.

Testing for Covid-19 has increased and exceeded a previous target of 10,000 per day, though later than the government initially promised.

Hancock’s bigger goal of carrying out 100,000 tests in England by the end of the month includes antibody tests – the fingerprick blood test that could be done at home. Hancock said he had bought 3.5m test kits and is known to have ordered millions more from nine companies, but the first tests to be put through validation at Oxford University have failed.

On Friday, after the latest figures revealed a further 684 people with the virus had died in the UK, Hancock said he was “absolutely determined to hit the new goal”.

But when asked about the IBMS warning at the Downing Street press conference, he acknowledged: “Yes, that will involve some challenges, there’s no doubt, including making sure we get hold of all of the parts and all of the reagents. And everybody can see there are challenges around the world.”

Allan Wilson, the IBMS president, said he did not understand the strategy. “Mixing antibody and antigen tests doesn’t add up to me,” he said. “We don’t have an antibody test that is any use at this stage so how can you include that in the 100,000 and not say what the mix within that 100,000 is of antibody and antigen tests? It’s just a bit of a muddle still.”

Wilson, the lead biomedical scientist in cellular pathology at his NHS trust, says they could deliver 100,000 tests for the virus every day – but only if they got the supplies that are currently either available only in tiny quantities or non-existent.

There are shortages of the test kits themselves, “but also of some very basic reagents, such as the virology transport medium that we need to put the swabs in. The actual swabs are in short supply – effectively they are rationed in my patch in Scotland but I know there are problems in England as well.”

The lysis buffer, used in extracting the RNA of the virus, was “in very, very short supply”, he said. So are precision plastics – “the little tubes and pipettes, so each test gets its own individual tube”. Those will not be available until mid-May.

“This is affecting countries across the world and there is nothing more the workforce can do to increase testing capacity any further,” said the institute in its statement. “We would urge caution as testing is ramped up to ensure that the supply chain is secured.

“The very real risk is that hospitals and pathology networks will run out of reagents and patients will not be able to be tested and this will not only impact upon their care but can lead to hospitals unable to manage all patients safely as has been seen in other countries.”

Charlie Swanton, the chief clinician of Cancer Research UK, who is turning the whole of the Francis Crick Institute into a testing lab, supports the government scaling-up of testing. However, he said his team were experiencing difficulties in obtaining test kits and even getting space on planes to have them delivered.

“We have some tests. We haven’t got enough yet,” he said. “We hope to secure our supply chain. We just need to get that in the institute building and then we will be happier. We don’t want to have to suddenly change the test three weeks from now. It is a constant worry. You’d be amazed how many blocks to the supply chain there are even in a simple diagnostic assay like this.”

Swanton, too, spoke of a global shortage of lysis buffer. “And then to make matters worse, because all the airlines have grounded their planes, there is no cargo space. So we’re having to solve all these problems. It’s like marshalling a small army. It’s been very tough.

“The other big problem is that we are competing, not just nationally but internationally for access to these reagents – and competing is a horrible term because we are all trying to help the same people. We’ve got to be very conscious of that in the UK, that we’re not depriving other hubs and other laboratories. But we hope to be able to share what we can.”

A handful of big companies, mostly based in the US, supply test kits for the virus with emergency approval from regulators in the US or EU. They include the Swiss pharmaceutical giant Roche, which has been in discussions with Public Health England (PHE) and is thought to be central to the plans for mass-testing in a new mega-lab in Milton Keynes.

Roche, credited with enabling up to 500,000 tests a week in Germany, has already opened three labs for PCR swab testing in Manchester, London and Gateshead, it emerged on Friday. It plans to open at least six more in the coming weeks for Public Health England with a lab in Wales opening on Monday and Northern Irish and Scottish sites to follow.

The government said on Friday it was already operating five testing sites for health workers including one in Boots headquarters in Beeston in Nottingham, and would expand the number of mostly drive-in sites to 50 in the coming weeks.

Doris Ann Williams, the CEO of the British In Vitro Diagnostics Association, said Johnson was himself calling the companies to try to increase UK supplies of testing kits.

“The pinch point is availability from the manufacturers of PCR test kits needed to work on their dedicated instrumentation. The prime minister is intervening with the global heads of the companies involved to understand when they may be able to supply more test kits,” she said.

The manufacturers were doing all they could, she said. “However, there is global demand and manufacturing capacity is being increased at pace, along with the logistics to distribute it but none of this can be achieved overnight.”