The health secretary apologised after photos published by the Sun showed him kissing Gina Coladangelo in his office on May 6, when people were still not allowed to meet or hug indoors.
Hancock acknowledged that he breached social distancing “guidance” but Downing Street refused to confirm whether or not he had broken his own laws.
Coronavirus laws in place at the time state that “no person may participate in a gathering” which “consists of two or more people” and “takes place indoors”, unless exemptions which do not appear to apply to Hancock and Coladangelo are invoked.
Labour and the Liberal Democrats have called for Hancock’s sacking, branding his position untenable.
But the prime minister backed Hancock to continue in his job.
A No.10 spokesperson told reporters: “The prime minister accepts the apology and considers the matter closed.”
But a Labour spokesperson hit back: “This matter is definitely not closed, despite the government’s attempts 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.
“The prime minister recently described him as ‘useless’ - the fact that even now he still can’t sack him shows how spineless he is.”
Hancock said he was “very sorry” for letting people down after the Sun published a CCTV image of him kissing Coladangelo.
The paper reported that the health secretary was having an extramarital affair with 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.
Downing Street insisted her appointment “followed all the correct procedures”.