Mr Cummings singled out Mr Hancock for his most stinging criticism, accusing him of lying and alleging he should have been sacked on 15 to 20 occasions.
Addressing the Commons on Thursday morning, the Cabinet minister responded: “These unsubstantiated allegations around honesty are not true. What we have done to handle this coronavirus pandemic has been unprecedented in modern times.
“Throughout, we have been straight with people, and straight with this House about the challenges that we as a nation face together. Of course, there were unprecedented difficulties that come with preparation for an unprecedented event.”
Mr Hancock repeatedly dodged questions when asked about the accusations at the Downing Street press conference on Thursday.
He was asked if Boris Johnson still had confidence in him as Health Secretary.
But Mr Hancock said he and the Prime Minister were focused on getting the country out of the Covid crisis.
He said: “That’s what we focus on, because that is what really matters to getting this country out of this pandemic.”
Mr Johnson, who faced claims from his former adviser that he was unfit for office, earlier denied Mr Cummings’ assertion that Government failings had resulted in tens of thousands of unnecessary deaths.
Asked whether those deaths were due to his “action or inaction”, Mr Johnson said: “No, I don’t think so.
“Of course this has been an incredibly difficult series of decisions, none of which we have taken lightly.”
He insisted that “at every stage we have been governed by a determination to protect life”.
Asked whether he said he would rather see “bodies pile high” than order a third lockdown, the Prime Minister said: “I have already made my position very clear on that point.
“I’m getting on with the job of delivering the road map that I think is the sensible way forward.”
Asked if Mr Cummings told the truth, Mr Johnson dodged the question.
One of the key claims made by Mr Cummings was that Mr Hancock lied about Covid-testing people before they returned to care homes in the early part of the pandemic.
Mr Cummings told MPs on Wednesday that the prime minister was furious to discover in April 2020 that untested hospital patients had been discharged to care homes, adding Mr Hancock had told the PM a month earlier they would be tested.
When asked about this claim, Mr Hancock told the Downing Street news conference on Thursday: “Of course we committed, and I committed, to getting the policy in place but it took time to build the testing.
“We didn’t start with a big testing system in the UK and then we built that testing system, and that’s why the 100,000 target was so important because it really accelerated the availability of testing because when you don’t have much testing we had to prioritise it according to clinical need.”
When pressed if he had told the prime minister and Mr Cummings in March 2020 that they would all be tested, Mr Hancock said: “My recollection of events is that I committed to delivering that testing for people going from hospital into care comes when we could do it.
“I then went away and built the testing capacity for all sorts of reasons and all sorts of uses, including this one, and then delivered on the commitment that I made.”
Meanwhile two of Britain’s leading coronavirus experts, Professor Neil Ferguson and Professor John Edmunds, backed up Mr Cummings’s central charge against the Government, that delays over imposing lockdowns were partly to blame for the high death toll.
In other key developments:
The scandal over deaths in care homes grew as a Cabinet minister admitted the Government could have acted “differently”. However, Housing Secretary Robert Jenrick blamed inaccurate advice from scientists that people without symptoms could not pass on the infection. His account was at odds with Mr Cummings’s claim that the Health Secretary promised all residents would be tested before going into homes.
Pressure mounted on the Prime Minister to speed up an official inquiry as a senior Conservative MP and doctor backed cross-party demands for it to launch no later than this autumn. Dr Dan Poulter told the Evening Standard that it must report back within 18 months in case of another pandemic.
Professor Ferguson said the Indian variant was now the “dominant strain”.
Mr Hancock did not respond to many of the allegations made by Mr Cummings. However, the Government faced a growing number of voices saying that many lives could have been saved.
Professor Edmunds, of the London School of Hygiene and Tropical Medicine, said a “very large number” of Covid-19 deaths could have been avoided in the second wave if the Government had taken more drastic action as being advised by scientists.
In his damning evidence to a joint session of the Commons health and science committees, Mr Cummings said on Wednesday: “Tens of thousands of people died who did not need to die.” He tore into Boris Johnson for not taking earlier and more decisive action in the autumn to stop the second wave, and for failings also as the pandemic hit Britain in the spring.
Asked whether a death toll running into the tens of thousands could have been avoided, leading epidemiologist Professor Edmunds told ITV’s Peston: “Well it depends what measures you put in place, what would be the alternative, but certainly if you did a significant package and you put it in place in September, then we would have averted many of the problems that we then subsequently had over the autumn wave.
“And that autumn wave of course fuelled the next wave because we allowed another variant (Kent) to escape and start to spread. So it’s hard to say how many cases and deaths would have been avoided but it’s a very large number.”
So far, 127,748 people have died in the UK within 28 days of testing positive for coronavirus, according to the Government’s official figures Professor Ferguson, from Imperial College London, whose modelling was instrumental in persuading the Government to bring in the first lockdown, said scientists had become increasingly concerned in the week leading up to March 13, 2020 about the lack of a clear plan, and 20,000 to 30,000 lives could have been saved with earlier action.
“I think that’s unarguable,” he told BBC Radio 4’s Today programme. “I mean the pandemic was doubling every three to four days in weeks 13th to 23rd of March, and so had we moved the interventions back a week we would have curtailed that and saved many lives”. Mr Johnson ordered the first lockdown on March 23.
Mr Cummings aimed his fiercest criticism at Mr Hancock over failings around care homes policy, personal protective equipment (PPE) procurement and his public pledge on a testing target which disrupted Whitehall.