Meanwhile, a think tank has reported the incident to the police, saying the footage was either illegally obtained or illegally leaked.
CCTV footage was published on Friday showing Hancock in an embrace with Gina Coladangelo, who had been taken on by the Department of Health and Social Care as an unpaid adviser on a six-month contract in March 2020, before being appointed as a non-executive director at the department.
Hancock, 42, has been at the centre of the government’s plan to fight against the CCP (Chinese Communist Party) virus pandemic, routinely telling people to follow strict rules and even welcoming the resignation last year of a senior scientist who broke restrictions in a similar manner.
Many considered Hancock’s extramarital affair his private business, but the breaking of guidelines has sparked accusations of blatant hypocrisy and the appointment of Coladangelo to a taxpayer-funded role has also raised questions.
Hancock apologised on Friday, saying he was “very sorry” for have let people down.
Downing Street on Friday said the matter was considered closed after Hancock’s apology and insisted the “correct procedure” had been followed in relation to Coladangelo’s appointment without going into details.
But the Daily Telegraph reported that Tory MPs were telling the prime minister to “pull the plug,” with public reaction over coming days key to his fate.
North Norfolk Conservative Duncan Baker became the first MP to openly call for Hancock to go on Saturday.
He told his local newspaper, the Eastern Daily Press: “In my view, people in high public office and great positions of responsibility should act with the appropriate morals and ethics that come with that role.
“Matt Hancock, on a number of measures, has fallen short of that. As an MP who is a devoted family man, married for 12 years with a wonderful wife and children, standards and integrity matter to me.
“I will not in any shape condone this behaviour and I have in the strongest possible terms told the Government what I think.”
A snap poll from Savanta ComRes, released hours after photographs of the pair kissing in Hancock’s ministerial office surfaced, found 58 percent of UK adults thought that Hancock should resign, compared to 25 percent who thought he should not.
And the COVID-19 Bereaved Families For Justice group, which represents those who have lost loved ones to the pandemic, also called for Hancock to go.
The Health Secretary is also deeply unpopular with some conservatives who believe that he has been an obstacle to the easing of CCP virus restrictions.
Meanwhile, the filming in a ministerial office and the leaking of such footage to media has raised a new set of ethical and security questions.
Think tank Henry Jackson Society has reported the disclosure of the footage to the Metropolitan Police as a breach of the Official Secrets Acts (OSA).
A spokesman for the group said: “It is clear that an offence has taken place under the Official Secrets Acts and that warrants investigation. Either a tape has been leaked in breach of obligations under the OSA or illegal access to a protected site has been obtained.”
The Met said it was “aware of the distribution of images alleged to have been obtained within an official Government premises,” but “no criminal investigation has been launched.”
“At this time this remains a matter for the relevant Government department,” the Met said.
The Cabinet Office said it would never comment on security issues but it is understood that no cross-Government probe has been launched so far.
PA and Reuters contributed to this report.