Matt Hancock leaving 10 Downing Street with Gina Coladangelo in May
The health secretary has been backed by Number 10 after he released a statement saying he had "let people down" and was "very sorry" after pictures emerged of him kissing an aide.
But a Labour spokeswoman said: "This matter is definitely not closed, despite the government's attempts to cover it up."
Questions about Mr Hancock hiring former lobbyist Gina Coladangelo surfaced after pictures in The Sun newspaper showed the health secretary, who is married, embracing the aide in his office.
Comment: Interesting tidbit from the Daily Mail: 'Ms Coladangelo's father Rino Coladangelo, 70, is chief executive of an international pharmaceutical company', and Sky News reports that her brother has a top job at a company with NHS contracts.
Facing questions from reporters at a regular Westminster briefing, the prime minister's spokesman did not say whether Mr Johnson had asked the health secretary to resign, nor if Hancock had offered the PM his resignation.
"You've seen the health secretary's statement, so I would point you to that. I don't really have anything further to add," he said.
"The health secretary set out that he accepted he had breached the social distancing guidelines and he has apologised for that.
Comment: Indeed he did - here's the CCTV footage:
"The prime minister has accepted the health secretary's apology and considers the matter closed."
The spokesman also refused to address suggestions that Mr Hancock had broken the law, repeatedly pointing reporters to the health secretary's statement.
According to The Sun, the images, which appear to be from CCTV footage, were taken on 6 May from the Department of Health and Social Care building.
At the time the picture was reportedly taken, guidance said people should keep their distance from anyone not in their household or support bubble.
Legislation in force at that point also said "no person may participate in a gathering" that "consists of two or more people... and takes place indoors".
There was an exception for "work purposes or for the provision of voluntary or charitable services", but it is not clear whether the health secretary believes the embrace was part of a work meeting.
Labour and the Liberal Democrats have called on the PM to sack the health secretary, but Mr Hancock made clear in his statement that he wants to continue.
Matt Hancock and Gina Coladangelo in 2019
Labour Party chair Anneliese Dodds said: "He set the rules. He admits he broke them. He has to go. If he won't resign, the PM should sack him."
Analysis: Sam Coates, deputy political editorLiberal Democrat MP Layla Moran, who chairs the all party parliamentary group on coronavirus, accused Mr Hancock of "utter hypocrisy" and questioned Mr Johnson's response - saying whether or not he accepted the apology was "irrelevant".
Downing Street is busy attempting to shut down the Matt Hancock controversy and is making clear they regard the matter as closed.
But there are plenty of grounds to think this issue won't go away that easily.
Number 10 knows the damage that can be done by stories that remind the public there can be one set of rules and assumptions kept by politicians - and another for everyone else.
Comment: This is true, except we're reaching the stage of corruption where the establishment and its ilk are brazenly showing - such as at the G7 - as well as announcing that the rules really do not apply to them: Minister says travel quarantine rules do not apply to 'important people'
As health secretary, Mr Hancock signed into law the regulations that he is accused of breaking.
It does not help that everyone is being invited to judge whether the kiss in The Sun was a "reasonably necessary" exception to the ban on indoor contact, the legal test laid down in the regulations.
Nor does it help that Mr Hancock was memorably quick to judge Professor Neil Ferguson when the then Sage scientist was found visiting his lover, and he later resigned.
Campaign group COVID-19 Bereaved Families for Justice said the PM's backing for the health secretary was a "slap in the face" for families who had lost loved ones to the virus.
"Up and down the country, bereaved families have been doing everything they can to follow the rules and prevent further loss of life," the group said.
Comment: Families were denied access to their loved ones for well over a year, some of whom were therefore forced to die alone.
"But it's clear Matt Hancock thought that 'hands, face, space' was a rule for everyone else."
Adam Wagner, a human rights barrister from Doughty Street chambers who has analysed COVID restrictions closely over the course of the pandemic, told Sky News it is "quite likely" the health secretary broke the law.
"Unlike any other country in Europe we were banning relationships effectively, banning people meeting up indoors," he said.
"So I'm absolutely certain if you'd asked Matt Hancock about this exact question, if somebody was at work and decided to have an affair with a co-worker, went and met in different places to have that affair, would that be within the law, he would have said no."
Mr Hancock's statement comes after he did not appear at a planned constituency event on Friday morning at Newmarket Racecourse.
Gina Coladangelo's LinkedIn page
Comment: Bojo gave his mistress contracts worth tens of thousands of pounds of tax payers: Scandal as UK's PM Boris Johnson accused of misappropriating public funds during extra-marital affair
Ms Coladangelo, who is listed on the department's website as a non-executive director, is the marketing and communications director at British retailer Oliver Bonas, which was founded by her husband Oliver Tress.
Her LinkedIn profile says she has been working as a non-executive director at the department since September 2020 and was at Oxford University at the same time as the health secretary.
Mr Hancock has been married to his wife Martha for 15 years and they have three children together.
Comment: RT reports: