Matt Hancock is facing calls to resign after being accused of having an affair with an adviser to his department.
The Sun published pictures of the married health secretary appearing to kiss his close friend Gina Coladangelo.
The images, apparently captured from CCTV footage, were taken on 6 May at the headquarters of the Department of Health and Social Care (DHSC), the newspaper adds.
Hancock has apologised, saying: "I accept that I breached the social distancing guidance in these circumstances. I have let people down and am very sorry."
But he has refused to quit, saying: "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.”
Liberal Democrat leader Sir Ed Davey said on Twitter: “The reason Matt Hancock should resign is that he is a terrible Health Secretary, not because of his private life."
Labour has said ministers are "entitled to a private life", but added: “However, when taxpayers’ money is involved or jobs are being offered to close friends who are in a personal relationship with a minister, then that needs to be looked into
The scandal has left Hancock open to accusations of hypocrisy.
Hancock last year said a government adviser who broke lockdown rules to have an affair should resign.
In May 2020, the health secretary claimed to have been left “speechless” when a high-profile government pandemic adviser, Professor Neil Ferguson, was found to have broken lockdown rules by arranging visits from his lover last year.
Hancock criticised Prof Ferguson’s “extraordinary” behaviour, and said it had been right for him to quit his role on the Scientific Advisory Group for Emergencies (Sage).
On Friday it was alleged that Hancock had engaged in a "steamy clinch" with aide Gina Coladangelo, and that the pair had been conducting an affair while working together at Whitehall.
The pictures of Hancock apparently embracing Coladangelo were taken on 6 May when social distancing in workplaces was mandatory – and two weeks before the ban on hugging between people from different households was lifted.
On 13 May - a week after the picture was taken - Hancock said advised people to be “careful” when hugging others ahead of restrictions on physical contact being lifted the following day.
"We should all be careful, we all know the risks. Outside is safer than inside, so even though you can from tomorrow, meet up inside, it’s still better to meet up outside," he said.
The married father also told Sky News on 16 May he planned to hug his dad the following day, “but we’ll probably do it outside and keep the ventilation going: Hands, face and space”.
Although Scotland Yard decided not to prosecute Prof Ferguson, Hancock had said he would back the police if they wanted to take action over his breach of restrictions.
“It’s extraordinary. I don’t understand,” the Hancock told Sky News at the time, when asked about Ferguson’s lockdown trysts.
“Professor Ferguson is a very eminent and impressive scientist and the science that he has done has been an important part of what we have listened to," he said.
Watch: Matt Hancock accused of affair with adviser to his department
“I think the social distancing rules are very important and people should follow them.
“I think that he took the right decision to resign."
On Friday, former minister for Europe Denis MacShane wrote on Twitter: “Hancock’s hypocrisy in urging police investigate Prof Neil Ferguson’s affair will come back to haunt.”
Political commentator Ian Dunt said Mr Hancock faced questions over the “straight up hypocrisy” of offering COVID guidance about telling others to avoid close physical contact with others.
Anneliese Dodds, the Labour chair, said that if Hancock had been having a relationship with Coladangelo it was “a blatant abuse of power and a clear conflict of interest”. She added: “His position is hopelessly untenable. Boris Johnson should sack him.”
Prof Ferguson was a member of Sage, the body that advises the government on policy in relation to COVID. Hancock as a minister is responsible for implementing the recommendations and creating government policy.
Hancock and Coladangelo met while studying at Oxford University and have remained "close" according to friends.
In spring 2020, just as the UK entered its first lockdown, Coladangelo was appointed as an unpaid adviser on a six-month contract at the Department of Health and Social Care (DHSC).
Then last September Hancock gave her a job as a non-executive director at DHSC, making her a member of the department’s oversight board.
The move hit the headlines as there was no public record of the appointment, which was set to see Coladangelo earn at least £15,000 of taxpayers’ money, potentially rising by a further £5,000.
In May of this year, Hancock was found to have committed a "minor breach" of the ministerial code when a coronavirus contract was awarded to his sister's company in which he had share holdings.
Lord Geidt, the independent adviser on ministers' interests, found that Hancock had made a "technical" breach of the ministerial code of conduct by failing to declare that a firm run by a family member, which he has a 20% stake in, had won an NHS contract.
And just two weeks ago Hancock was left red-faced after WhatsApp messages were leaked by former Downing Street adviser Dominic Cummings, which appeared to show Boris Johnson labelling him "f***ing useless".
Yahoo News UK has contacted the DHSC for comment but had received no response at the time of publishing.
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