Mr Hancock failed to appear in the Commons on Wednesday and is fighting claims he rejected advice to give coronavirus tests to all residents going into English care homes.
The allegations are based on a leaked trove of more than 100,000 WhatsApp messages obtained by the Daily Telegraph, giving an insight into the way government operated at the height of the Covid-19 crisis.
At Prime Minister’s Questions, Sir Keir Starmer called for Mr Sunak to ensure the inquiry had all the support it needed “to report by the end of this year”.
The Labour leader said: “Families across the country will look at this, and the sight of politicians writing books portraying them as heroes will be an insulting and ghoulish spectacle for them.
"The country deserves better. The Covid inquiry has already cost the taxpayer £85 million and hasn’t heard from a single government minister yet. So can the Prime Minister assure the House no more delays, that the inquiry will have whatever support it needs to report by the end of this year?”.
Mr Sunak responded: “Rather than comment on piecemeal bits of information, I’m sure the honourable gentleman will agree with me the right way for these things to be looked at is the Covid inquiry.
“There is a proper process to these things. It is an independent inquiry, it has the resources it needs, it has the powers it needs, and what we should do in this House is to let them get on and do their job.” However, Mr Sunak notably declined to say the report should be completed this year.
Mr Hancock is now considering legal action, while strenuously denying claims he rejected advice to give coronavirus tests to all residents going into English care homes while health secretary.
Allies alleged the messages, leaked by journalist Isabel Oakeshott after she was handed them by Mr Hancock while working on his Pandemic Diaries memoir, have been “spun to fit an anti-lockdown agenda”.
Mr Hancock’s spokesman said claims he rejected clinical advice on care home testing was “flat wrong” because he was told it was “not currently possible” to carry out the tests. Downing Street suggested a leak inquiry was not required because the source had been publicly identified.
The Prime Minister’s official spokesman said: “Leaks regarding data protection issues are a matter for the information commissioner. We take leaks seriously, we don’t comment on them.”
As part of the leak of Mr Hancock’s WhatsApp messages, it is claimed the health secretary helped get a test sent to Jacob Rees-Mogg’s home even as others across the country struggled to access testing.
The Liberal Democrats have now written to the Prime Minister to ask him what he knew and when regarding claims that ministers had access to “priority testing”.
Deputy Lib Dem leader Daisy Cooper said: “These reports are just more evidence that it’s one rule for Conservative ministers and another for everyone else.
“The Government must urgently publish exactly how many Conservative ministers, MPs and their families had access to priority testing when the public faced a national test shortage.”