Some of the UK’s biggest care home operators have told the Guardian they repeatedly warned Matt Hancock’s department about the risk of not testing people discharged from hospitals into care homes in March 2020.

Their claims are likely to increase pressure on the health secretary when he appears before MPs on Thursday to defend his handling of the Covid pandemic to a parliamentary inquiry.

Care England, which represents the largest private chains where thousands of people died in the first months of the virus, told the Guardian it raised “the lack of testing in hospitals and in the care sector” several times in correspondence with the Department of Health and Social Care (DHSC) as well as NHS England in late March 2020.

The Care Provider Alliance also called on the government to prioritise testing for care residents to stop the spread of the virus, warning on 26 March 2020 that without it “there is no way of knowing whether they are going to infect others”.

It also emailed Hancock directly saying: “All people discharged from hospital to social care settings … MUST be tested before discharge.”

Yet despite the pressure from frontline care operators, Hancock didn’t make testing for hospital discharges mandatory until mid-April, after the first wave death toll had peaked weeks later.

The care homes issue is likely to be a key focus of questions when Hancock faces cross-examination from MPs on the combined health and social care and science and technology committee inquiry on Thursday.

Hancock’s testimony comes two weeks after Dominic Cummings, the prime minister’s former adviser, accused him of serial incompetence that should have led him to be sacked.

He also alleged Hancock had in effect misled Downing Street into believing that testing on patients being sent to back to care homes was being carried out when it wasn’t.

Hancock denies this, saying that his position was that hospital discharges would be tested only when enough testing became available.

The UK already had capacity for 10,000 daily tests at the start of April 2020. Between 17 March and 15 April, when tests were finally required before admission into care homes, about 25,000 people were discharged from hospitals into facilities, the National Audit Office has found.

Pete Calveley, the chief executive of Barchester, which lost 1,100 residents to Covid over the pandemic, told the Guardian that in March and April “we were saying absolutely no one should be discharged from hospital without a negative test” and that message was conveyed to the DHSC via Care England.

Representatives of smaller care home groups also said they were “consistently” urging testing of discharges earlier on when it was not happening.

“To officials and the minister for care we were saying that people were being discharged out of hospitals into care homes untested,” said Nadra Ahmed, the chair of the National Care Association, which represents independent care providers.

“We were raising the issue with the department on a regular basis. One of our questions was, ‘What are you doing after you test someone [before they are discharged]. Are they in an isolation wing?’”

Cummings told the select committee inquiry last month that “we were assured that the people who were being sent out would be tested” and that “it was only in April after the prime minister and I had both ourselves been ill, that we realised that what we were told would happen never did happen, or only happened very partially and sporadically.”

However, only weeks later, on 13 May, Johnson told the Commons: “We had a system of testing people going into care homes.”

The issue of testing has become highly charged and Hancock is facing a high court hearing in October over an allegation from a bereaved relative of a deceased care home resident that the government breached the Human Rights Act and the Equality Act when their policies allowed people to be discharged into care homes without being tested.

The government last month produced figures which suggest only 1.6% of care home outbreaks in the first six months of the pandemic were caused by infected people being discharged from hospitals. They imply that transmission from the community was a far greater cause of the devastation in social care. But the data has been dismissed by care operators, which point out that only some people were being tested so it is impossible to know that.

Calveley, who said two-thirds of his 240 care homes were infected, added: “It beggars belief to say it wasn’t the residents coming back and it must have been staff, because no one was being tested.”

He said that Barchester homes with block bookings to take hospital discharges had outbreaks and that hospitals sent residents back in ambulances unannounced, sometimes with Covid symptoms.

A DHSC spokesperson said that in February 2020 “the scientific understanding did not suggest asymptomatic individuals posed a significant risk in terms of transmission. Those with symptoms would have been tested on admission or during a hospital stay and were isolated accordingly.”

They added: “Further guidance was issued on 19 March 2020 setting out how we would continue to support the safe and timely discharge of people who no longer needed to stay in hospital. Throughout this time, government worked tirelessly to build a national testing system from scratch, the result of which is that everybody who needs a test can now get one.”