The health secretary spoke days after the High Court ruled the government unlawfully failed to publish details of billions of pounds’ worth of coronavirus-related contracts.
Mr Hancock has said legal cases about transparency returns were “second order” to saving lives and said his officials had been working long hours to procure PPE instead.
In a torrid interview, he also claimed the NHS was “very close” to running out of PPE but prevented the worst thanks to his team - despite desperate shortages across the country.
He had said this was justification for his decision to press ahead with contracts, which Good Morning Britain presenter Piers Morgan described as a "barefaced lie."
“There were areas where it was enormously challenging and there were areas where there were problems but we never had a national outage of it, we were very close to that,” he told Good Morning Britain.
“We never had a national outage of it because of my team and the work they were doing.”
Rosena Allin-Khan, Labour's shadow minister for mental health, an NHS A&E doctor who worked on the frontline during lockdown, accused Mr Hancock of "trying to rewrite history".
She said: "It is an insult to claim there was no shortage of PPE.
"Many frontline workers had to ration protective equipment, putting themselves at risk.
"Lots of it was inadequate and poorly fitting, and some NHS staff had to make gowns themselves from bin bags.
"The fact is, it was a smash-and-grab for Tory donors and friends. And protecting workers who were putting themselves in harm's way to look after people seems to have been an afterthought."
The government came under widespread criticism at the beginning of the pandemic last year, with some medics resorting to using bin liners instead of aprons and many blaming NHS staff deaths on PPE shortages.
Mr Hancock has faced calls for greater accountability after a judge said he did not publish redacted contracts in accordance with the transparency policy.
Despite the criticism, he told GMB: “I think we should be on this programme thanking my team, they worked so hard.”
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Mr Morgan rebuked him: “You and your team have presided over a woeful handling of this pandemic that has led to us having the worst death toll in Europe, 130,000 dead.
“So I’m sorry if my first thought when you come on, Health Secretary, is not to thank you and your team.”
Figures from the UK's statistics agencies for deaths where Covid-19 has been mentioned on the death certificates show that there have been more than 130,000 coronavirus related deaths in the UK.
The latest government figures show there have been 120,757 deaths within 28 days of a positive Covid test.
Facing several calls to apologise after the court ruling, Mr Hancock once again refused.
“I won’t apologise because to apologise would imply that I’d do something differently,” he said.
“And, given the choices we were faced with in April and May when there were very, very serious problems with access to PPE and some people were going without and the team were working so hard… to have taken some of the team off that lifesaving work in order to complete the paperwork on time instead of just [being] over a fortnight late that would have been wrong.”