Mr Hancock faced questions in the House of Commons a day after prime minister Boris Johnson's former adviser Dominic Cummings delivered a devastating string of allegations over the government's handling of the pandemic in evidence to a parliamentary inquiry.
Mr Cummings told a joint inquiry by the House of Commons health and social care and science and technology committees on 26 May that tens of thousands of people had died needlessly during the COVID-19 pandemic - and that Mr Hancock was 'certainly one' of the senior figures in government who had performed 'disastrously' below the level the public had a right to expect.
He accused the health secretary of lying to the public and to cabinet colleagues, blaming NHS chief executive Simon Stevens and chancellor Rishi Sunak for PPE shortages - and said that claims a 'protective shield' had been thrown around care homes had been 'complete nonsense'.
Challenged to respond to the claims by shadow health secretary Jonathan Ashworth, Mr Hancock told MPs: 'These allegations are serious and I welcome the opportunity to come to the House and put formally on the record that these unsubstantiated allegations around honesty are not true.
'I have been straight with people in public and private throughout. Every day I have got up and asked what must I do to protect life. That is the job of a health secretary in a pandemic. We have taken an approach of openness and transparency.'
The health and social care secretary said he had made statements in the House of Commons on around 60 occasions, and along with the prime minister had delivered 84 press conferences from Downing Street.
He added: 'What matters remains the same. Getting vaccinated, getting tested, delivering for our country, overcoming this disease and saving lives. And that is what matters to the British people.'
Mr Hancock also told MPs in response to further questions that it was 'true that the Indian variant is spreading across the country' - and that it remained too early to say whether the next stage in easing of restrictions imposed during the pandemic could go ahead in June.
Labour shadow health and social care secretary Mr Ashworth pointed to the allegations from Mr Cummings - that delays in the government's pandemic response had cost lives, and claims about dishonesty by Mr Hancock.
He said: 'Either these allegations are true, and the secretary of state potentially stands in breach of the ministerial code and the Nolan principles, or they are false and the PM brought a fantasist and a liar into the heart of Downing Street. Which is it? Families who have lost loved ones deserve full answers.'
Mr Ashworth asked the health and social care secretary: 'Is he ashamed that he promised a protective shield around care homes and over 30,000 care home residents have died? Why were 25,000 elderly people discharged from hospital into care homes without any tests?
'Did he tell Downing Street in March that people discharged from hospital had been tested even though it wasn't until 15 April that there was a requirement that testing take place?'
The Labour shadow minister said Mr Hancock's department had been responsible for securing adequate PPE and had failed to deliver. He pointed out that 850 healthcare workers had died during the pandemic, asking: 'How many could have been saved if they had had PPE?'