Hospital leaders have launched a strident attack on the government’s coronavirus testing strategy, as it became clear that the target of 100,000 daily tests by 30 April would be comprehensively missed.

NHS Providers, which represents foundation trusts in England, rounded on ministers for “a series of frequent tactical announcements” to expand testing criteria, and dismissed the 100,000 target as a “red herring” that distracted from their failures.

Just 33,000 people were tested for Covid-19 in the latest 24-hour period – a record high for a single day – according to official figures. Dominic Raab, the first secretary of state, said that more than 52,000 tests were carried out, but this total is apparently bolstered by 19,000 retests.

Test capacity was now more than 73,000 a day, he said – still considerably below the target set by the health secretary, Matt Hancock, at the start of April.

Comprehensive testing – combined with tracing those who have come into contact with sufferers, and containing the spread through careful self-isolation – has been described as the route out of lockdown while avoiding a serious second peak. On Wednesday ministers confirmed that total UK coronavirus deaths had exceeded 26,000.

In recent days, testing has been expanded from hospital patients and NHS workers to key workers and, on Tuesday, to all symptomatic over-65s, those who need to go out to work, care home residents and staff. The swab tests can be booked online and carried out at drive-through test centres or using home kits.

NHS Providers said in a report released on Wednesday: “NHS trust leaders believe they have done all they can to support the national testing effort so far but are increasingly frustrated with the lack of clarity on how the testing regime will be developed for this next phase.

“At the moment they feel they are on the end of a series of frequent tactical announcements extending the testing criteria to new groups with no visibility on any longer term strategy, and are being expected at the drop of a hat to accommodate these changes with no advance notice or planning.”

Q&A What is contact tracing? Show Hide Contact tracing is one of the most basic planks of public health responses to a pandemic like the coronavirus. It means literally tracking down anyone that somebody with an infection may have had contact with in the days before they became ill. It was – and always will be – central to the fight against Ebola, for instance. In west Africa in 2014-15, there were large teams of people who would trace relatives and knock on the doors of neighbours and friends to find anyone who might have become infected by touching the sick person. Most people who get Covid-19 will be infected by their friends, neighbours, family or work colleagues, so they will be first on the list. It is not likely anyone will get infected by someone they do not know, passing on the street. It is still assumed there has to be reasonable exposure – originally experts said people would need to be together for 15 minutes, less than 2 metres apart. So a contact tracer will want to know who the person testing positive met and talked to over the two or three days before they developed symptoms and went into isolation. South Korea has large teams of contact tracers and notably chased down all the contacts of a religious group, many of whose members fell ill. That outbreak was efficiently stamped out by contact tracing and quarantine. Singapore and Hong Kong have also espoused testing and contact tracing and so has Germany. All those countries have had relatively low death rates so far. The World Health Organization says it should be the “backbone of the response” in every country. Sarah Boseley Health editor

Chris Hopson, its chief executive, added that the 100,000 target may have a “galvanising effect” but “what matters most is an updated strategy to take us through the exit from lockdown”.

He added: “Trusts stand ready to play their part in delivering that new testing regime, but they need to know a lot more, as quickly as possible, to play that part effectively.

“The NHS has achieved so much in confronting the challenges posed by coronavirus. However testing is one area where, despite all the work delivered by trusts and the NHS, the health and care system as a whole has struggled to develop an effective, coordinated approach.

Further criticism came from Andy Burnham, the mayor of Manchester, who said the goal had been set and driven forward without local consultation. Burnham, a health secretary in Gordon Brown’s government, said the drive to hit the target had been done in a “haphazard way” without local consultation.

At a meeting of the region’s Covid-19 emergency committee on Wednesday, he welcomed the increase in testing capacity but warned a more strategic and co-ordinated approach was needed.

“Lots of frustration [was] expressed at the meeting about arrangements for testing and what feels to people to be a confused picture across Greater Manchester with different capacity and overlapping schemes, and still capacity being put in without any reference to local authorities,” he told a press conference.

“It feels to us as though the government has been chasing the target on testing without fully thinking through the strategy at a local level and involving local leaders.”

Prof John Newton from Public Health England (PHE), who has been charged with increasing testing numbers, has said he is confident the 100,000 daily target will be met on time once numbers are finalised.

With just one day to go, there was evidence of a significant push to increase the numbers and hit the goal.

Hancock urged a wider range of people to apply for tests in an email sent out from Conservative central office. The over-65s or anyone who has to go out to work – or their families – could apply online for a test if they had symptoms. “This means construction workers to emergency plumbers, research scientists to those in manufacturing – can now be tested,” he said.

Facebook Twitter Pinterest Matt Hancock, the health secretary, set the target at the beginning of April. Photograph: Kirsty O’Connor/PA

On Twitter, the department gave locations of the mobile testing units. “If you’re eligible for a test and near one of these sites you can book in now,” it said.

A Guardian analysis of the data suggests that around 20% more tests are carried out each day than there are people tested. On Tuesday, that rose to a high of 37%. The reasons are unclear, but it is known that retests because of results that doctors disbelieve are not uncommon. In hospitals, that can be because doctors are convinced a patient has Covid-19 and do not believe a negative result, so get the test repeated.

Although the lab processing is very accurate, getting enough swab sample of the virus from the back of the mouth or nose can be difficult. PHE said that originally people with symptoms would have a swab test of the back of the mouth and another one of the nose, but now there is a move to obtaining just one sample. That might mean a greater likelihood of retesting.

The government is not keeping a record of the number of inconclusive tests but, according to a departmental spokesperson, these are rare.

As of 9am on 29 April 818,539 tests had been carried out on 632,794 individuals, meaning 23% of all tests carried out to that date were retests.

A spokesperson for the Department of Health and Social Care said that some people are tested more than once for clinical reasons. “The number of people tested is the number of new people tested each day,” he said. “The number of overall tests could include the same person tested multiple times, hence the widening gap.”