The health secretary twice totally refused to engage with questions on the issue before being challenged on his responses by Mirror deputy political editor Ben Glaze.
In response, Hancock suggested the media should only ask questions that the government decides “really matter”, while insisting the Downing Street press conference he was hosting was only about coronavirus.
At previous press conferences, ministers have been happy to answer questions on wider issues affecting the government.
It came after the Electoral Commission said “there are reasonable grounds to suspect that an offence or offences may have occurred” as it launched a probe into the refurbishment of the prime minister’s flat.
No.10 has refused to say whether Johnson sought an initial loan from the Conservative Party to cover a reported £58,000-worth of renovations to his residence in No. 11, which he shares with partner Carrie Symonds and their baby son Wilfred.
Political donations have to be declared to ensure there are no questions or concerns over politicians or parties being unduly influenced by those giving them money.
At a Downing Street press briefing, BBC political editor Laura Kuenssberg asked Hancock whether a serving government minister who is found to have broken party funding rules should resign.
But the health secretary replied: “I know that the prime minister answered lots of questions about this in the House of Commons earlier and given that this is a coronavirus press conference you won’t be surprised I’m not going to add to the answers the prime minister has already given to very extensive questioning, thanks.”
Times Whitehall editor Chris Smyth then asked two questions on Covid before enquiring whether the government was still threatening to abolish the Electoral Commission.
Hancock replied: “I think we’ll give the third one [question] a miss.”
The health secretary was then challenged over his approach by Glaze.
The Mirror journalist said: “As culture secretary, you championed the right of the free press and fourth estate to ask difficult questions.
“Yet this evening you haven’t engaged with those questions from Chris or from Laura around Tory sleaze.
“Now what’s the point in us being able to ask difficult questions if you’re not going to engage with them?”
Hancock replied: “The point of the press conference is the incredibly important progress that we’re making about coronavirus, which is without doubt the most important thing facing the country.
“And if you’ve listened to the answers, I’m sure you have... you will have one of the most illuminating descriptions of where we are up to scientifically, and operationally and clinically that is available, and I’m very, very grateful to the incredible capability of people who support me as a minister.
“It is important there are questions and there were endless questions in the House of Commons earlier on some of the issues that you’ve raised, and you will have seen the appointment of [new independent adviser on ministerial interests] Lord Geidt earlier.
“But you’ve also got to concentrate on the big things that really matter.”
Earlier this month, Boris Johnson was accused of breaking ministerial rules when he used a televised briefing on the Covid pandemic to launch an “unprompted political attack” on London mayor Sadiq Khan about the Transport for London budget.