Two of the UK’s biggest care home operators have reported falling death rates from Covid-19, raising hopes that outbreaks which have devastated some of the most vulnerable and elderly people may finally be abating. The number of residents who have recovered from the virus has now eclipsed the numbers of deaths from it across 220 care settings operated by MHA, the largest charitable provider of homes, which by Monday had recorded 359 deaths in total. It said fatalities peaked around 22 April and have fallen gradually since. Meanwhile HC-One, the largest commercial operator which has lost 829 residents to confirmed or suspected Covid-19, said deaths had fallen from a peak of 31 a day on 19 April to four on Monday. A manager at a separate nursing home, in Ealing, where 27 residents were killed in an outbreak in April told the Guardian she had recorded no new infections for a fortnight. The positive signs came ahead of the publication on Tuesday of official figures for care home deaths to 1 May, which are expected to show an increase on the 5,890 fatalities recorded in England and Wales so far to 24 April. The daily numbers of dead notified by care homes to the Care Quality Commission regulator and published by the Office for National Statistics declined in the last five days for which data was available. Alongside the more up to date operators’ figures, they offer hope the peak of the first wave of the virus may have passed in many care homes. But there were warnings that unless testing of care staff and residents is urgently improved there could be a second peak in fatalities, potentially coinciding with the autumn flu season. There have been complaints from homes that they are unable to access testing kits and tests that are being carried out are not being properly processed, rendering them worthless. The government’s long-promised Amazon-style “Clipper” system to dispatch personal protective equipment is still not up and running nationally. A GP in Cheshire said tests carried out at one care home were simply not collected for processing, while Jess Phillips, the MP for Birmingham Yardley tweeted: “A Birmingham care home, 30 tests sent and done. No one ever came to pick them up, so they went in the bin. No one got tested.” In Oxford, John Guy, chairman of the trustees of the Fairfield care home, said: “As of yesterday we still have not received any swabs to do the home testing of residents which we first requested on 27 April when Matt Hancock said that home testing was available.” After Boris Johnson promised in his Sunday evening TV address that more would be done in the wake of “awful epidemics” in care homes, the government announced on Monday that by 6 June, every care home for the over-65s would have been offered testing for residents and staff. It said that by the end of this week the NHS would also supply a named contact to help train care home staff – including in infection control – and that each home would be allocated a named clinician, a reflection of concern that care staff, who are not medically trained, have struggled to cope with the new virus. “We need constant vigilance to avoid a second spike,” said Sir David Behan, chief executive of HC-One, adding that “targeted and sustained testing” is needed to maintain the lower levels of fatalities in its homes. “We need to avoid it coinciding with the normal onset of seasonal flu in autumn which would be a double whammy,” he said. Limiting use of agency care staff who might spread infection and keeping bank staff to shifts in a single home helped bring fatalities down, alongside a reduction in the number of people being infected in wider society, he said. “We are starting to see the slowing down of cases of Covid-19 and the number of recoveries is now well above that of the residents we have sadly lost to the virus,” said Sam Monaghan, chief executive of MHA. “That doesn’t mean we can be complacent. The threat of coronavirus is still present and we need to make certain that routine testing is fully in place, not just where residents and staff are showing symptoms but on a weekly basis.”