Matt Hancock was asked why he had not offered to resign during a 20-minute interview with presenters Piers Morgan and Susanna Reid this morning.
His appearance on the programme brought to an end a 201-day ‘boycott’ from Government ministers joining the breakfast TV show for an interview.
It follows the departure of Prime Minister Boris Johnson's top aide Dominic Cummings and director of communications Lee Cain from Downing Street this week.
Before Mr Hancock's interview began, the GMB presenters considered what had changed for them to secure a first ministerial interview since April.
Mr Morgan said: "Is it those two little sewer rats Cummings and Cain being thrown out of Downing Street? Oh, what a coincidence."
Kicking off the intense questioning of Mr Hancock, the controversial TV presenter asked him "Where the hell have you all been for the last 201 days?".
He added: "Do you think it's right and proper that in the biggest health crisis this country has faced for 100 years, that you as health secretary and the entire cabinet and the Prime Minister have boycotted a big morning breakfast television programme, and our viewers, for six months?"
Mr Hancock replied: "We haven't been away. I've been ... working incredibly hard."
"I'm here to answer all the questions that you might have on behalf of your viewers," Mr Hancock added.
Reviewing the last six months, Mr Morgan reeled off a "charge sheet" that he said revealed a "constant series of failures and U-turns throughout this year".
These ranged from the lack of personal protective equipment for health workers to the delay in introducing the first lockdown and the "complete shambles" of the Government's testing system.
"Given that we now have over 50,000 deaths in this country, which is the worst death toll in the whole of Europe, why are you still health secretary? Why haven't you offered your resignation?"
Mr Hancock said the Government had been "building the response to all of these enormous challenges of this unprecedented pandemic", picking out testing from Mr Morgan's "long list" where the health secretary insisted his targets had been met.
But Mr Hancock also admitted "we've made mistakes", citing guidance which was interpreted as preventing spouses attending the funerals of someone who died with coronavirus.
"That was wrong and we changed it," Mr Hancock said.
The health secretary also suggested that knowledge of the asymptomatic transmission of Covid-19 explained changes to rules for care homes.
Mr Morgan asked Mr Hancock whether it was "morally conscionable" that health workers may have to pay hospital parking charges after the end of the Covid-19 pandemic.
The health secretary said: "There are not those charges now. And there will not be during this pandemic. Once the pandemic is over, then we will no doubt return to this question."
Mr Hancock was also asked if he would like to "rethink" the support he expressed for Mr Cummings when he faced scrutiny over a trip to County Durham during the first lockdown.
The health secretary responded: "I'm not going to get into that, what I care about is the future."