Will Boris Johnson sack Matt Hancock, the Opposition Labour Party asked on Friday, after the Sun published pictures of Britain’s health secretary in a “passionate clinch” with a close aide, Gina Coladangelo, whom he has known since their Oxford days.

Hancock apologised after admitting breaking social distancing rules but said he would not be resigning: “I accept that I breached the social distancing guidance in these circumstances. I have let people down and am very sorry. I remain focused on working to get the country out of this pandemic, and would be grateful for privacy for my family on this personal matter.”

A spokesman for Boris Johnson said the Prime Minister had accepted Hancock’s apology and had full confidence in him. “(He) considers the matter closed,” he said.

Hancock’s departure at a critical time in the battle against Covid cannot be ruled out. A Conservative MP told the Daily Telegraph: “His position is completely unsustainable. Boris cannot afford to expend any more political capital on Matt Hancock. Boris should chop him immediately — today.”

The Sun said the CCTV images — leaked almost certainly by disgruntled employee possibly for a hefty fee — were recorded around 3pm on May 6 in a deserted corridor outside Hancock’s offices.

The whistleblower told the Sun it was “shocking that Mr Hancock was having an affair in the middle of a pandemic with an adviser and friend he used public money to hire”.

In Westminster it is not unusual for politicians to be become involved with colleagues since they work long hours away from home. But Hancock’s extra-marital affair might become a distraction when the country is still coping with the Covid crisis.

Labour Party chairwoman Annaliese Dodds demanded Hancock’s head on a platter: “If Matt Hancock has been secretly having a relationship with an adviser in his office — whom he personally appointed to a taxpayer-funded role — it is a blatant abuse of power and a clear conflict of interest.”

She added: “The charge sheet against Matt Hancock includes wasting taxpayers’ money, leaving care homes exposed and now being accused of breaking his own Covid rules. His position is hopelessly untenable. Boris Johnson should sack him.”

The Mail posed the question: “Will Boris Johnson sack Matt Hancock despite his affair with (American) Jennifer Arcuri and the PM’s own chequered love life? Some have suggested that the PM’s own chequered love life, including a series of affairs might prevent him giving the health secretary the push.”

On Friday the government wheeled out the transport secretary Grant Shapps to deal with the political fallout from Hancock’s affair.

He did a round of the studios repeating the same message that the images of Hancock “hugging and kissing” Coladangelo constituted an “entirely personal matter” — a form of words governments traditionally use when newspaper stories about an affair are basically true.

Coladangelo, 43, whose father is Italian, also works in the private sector. She is a director in the fashion firm Oliver Bonas founded by the millionaire Oliver Tress, who is her second husband. The couple have three children. She is a major shareholder and director of the lobbying firm Luther Pendragon.

Since last year she has been an adviser and non-executive director at the department of health. The role comes with a £15,000 salary and involves 15-to-20 days of work per year. But it gives her access to the corridors of power.

A department of health spokesman said: “This appointment was made in the usual way and followed correct procedure.”Hancock, 42, and his osteopath wife, Martha, 44, also an Oxford contemporary and granddaughter of an earl to whom he has been married for 15 years, have three children, one adopted. The tabloids noted that Hancock’s “humiliated wife”, was still “wearing her wedding ring” as she left home but “looked sad”.

Hancock found himself at the centre of a political firestorm recently after Dominic Cummings published text messages from the Prime Minister in which Boris referred to the his health secretary as “totally f****** hopeless”.

In May last year, epidemiologist Prof. Neil Ferguson resigned from the government’s scientific advisory group (SAGE) after it emerged he had broken lockdown rules when a married woman he was reportedly in a relationship with visited his home.

Hancock called Ferguson’s actions “extraordinary”, adding that social distancing rules were “there for everyone” and were “deadly serious”.