Boris Johnson has rejected calls to sack Matt Hancock after the Health Secretary admitted breaching the Government’s rules on social distancing.

Mr Hancock apologised after images emerged of him kissing a close aide who he appointed in his office at the Department for Health and Social Care (DHSC).

Labour said that his position had become “hopelessly untenable” and called for him to be sacked if he was not prepared to not quit voluntarily.

However a Downing Street spokesman said that Mr Johnson had accepted Mr Hancock’s apology and “considers the matter closed”.

Mr Hancock said he was “very sorry” for letting people down after The Sun published a CCTV image of him kissing Gina Coladangelo.

The paper reported that the Health Secretary was having an extramarital affair with Ms Coladangelo, who he knew from their days together at Oxford University and who he appointed to the DHSC last year.

She was initially taken on as an unpaid adviser on a six-month contract in March last year, before being appointed as a non-executive director at the department.

In a statement, Mr Hancock said: “I accept that I breached the social distancing guidance in these circumstances, I have let people down and am very sorry,” he said.

“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.”

Labour Party chair Anneliese Dodds said if Mr Hancock had been secretly having a relationship with an adviser he appointed to a taxpayer-funded role, it was “a blatant abuse of power and a clear conflict of interest”.

She said his admission that he had breached the rules on social distancing meant his position in office was no longer tenable.

“He set the rules. He admits he broke them. He has to go. If he won’t resign, the PM should sack him,” she said.

Despite Mr Johnson’s determination to defend his minister, Labour insisted it would continue to pursue the matter and would not allow the Government simply to “cover it up”.

“Matt Hancock appears to have been caught breaking the laws he created while having a secret relationship with an aide he appointed to a taxpayer-funded job,” a spokeswoman said.

However, the Metropolitan Police said they were not investigating Mr Hancock.

A spokesman said: “As a matter of course, the MPS is not investigating Covid-related issues retrospectively.”

The force had also not launched any investigation into how the CCTV showing the embrace had been made public.

During a testy briefing for journalists at Westminster, a No 10 spokesman repeatedly stonewalled in the face of reporters’ questions.

The spokesman insisted the “correct procedure” had been followed in relation Ms Coladangelo’s appointment but refused to go into detail or to say whether Mr Hancock had declared their relationship to senior officials at the DHSC.

Pressed repeatedly on whether their breach of social distancing rules amounted to a breach of the law, the spokesman said: “I point you to the Health Secretary’s statement. I have nothing to add to that.”

The row carries echoes of the political storm which erupted last year when Mr Johnson’s then top adviser Dominic Cummings made his infamous trip to Castle Barnard in County Durham in apparent breach of lockdown rules.

On that occasion, the Prime Minister resisted calls for Mr Cummings to be sacked despite widespread public anger over his actions.

Mr Johnson also rejected calls to fire Home Secretary Priti Patel when she was found to have bullied civil servants working for her, and he appears to be determined to do the same with Mr Hancock.

Professor Stephen Reicher, a government behavioural science adviser on the Spi-B committee, said the Prime Minister sticking by aides and ministers who may have breached the rules was what made the repercussions for restriction compliance “toxic”.

He told the BBC’s Newsnight programme: “The thing about this Cummings affair which made it truly toxic was not what Dominic Cummings did himself, it was when the Prime Minister defended him and therefore an individual indiscretion turned into a systemic issue, a sense of there’s one rule for us and another rule for them.

“And so for me, the Hancock affair changed when again, the Prime Minister rode in and defended him, again giving rise to that sense of it you are one of the Government, an adviser or minister, you’re treated in one way, but the rest of us are treated differently.

“And once you have a sense of them and us, it critically undermines trust, you have a sense of the Government as not looking after us, on our side, but as other, as imposing on us.”

The Health Secretary has also faced accusations of hypocrisy after he roundly condemned Professor Neil Ferguson, one of the Government’s leading advisers on the pandemic, when it emerged last year that he had met his lover in breach of lockdown rules.

The latest disclosures come at a difficult time for Mr Hancock after he was roundly attacked by Mr Cummings, who blamed him for problems in the early days of the pandemic with PPE and the spread of the disease to care homes.

The Health Secretary is also deeply unpopular with some Tory MPs who believe that he has been an obstacle to the easing of coronavirus restrictions.

Mr Hancock, who is reported to have met Ms Coladangelo when they both worked on the student radio station at Oxford, has been married to his wife Martha for 15 years, and the couple have three children.

Ms Coladangelo is the marketing and communications director at Oliver Bonas, a British retailer founded by her husband, Oliver Tress.

Vaccines minister Nadhim Zahawi voiced support for Mr Hancock, telling reporters: “The Secretary of State has apologised and has said everything he needs to say.”