The PM’s spokesperson said Mr Johnson had accepted his minister’s apology and considered the matter “closed”.
On Friday, Mr Hancock said he was “very sorry” for breaching social distancing guidelines but made clear he did not intend to resign over the matter.
“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,” the health secretary said.
The Sun claimed Mr Hancock was caught on camera kissing Gina Coladangelo, with the newspaper publishing security pictures reportedly taken on 6 May.
The publication later released a minute-long video of the clinch, as well as a photograph of the pair reportedly enjoying a meal at a west London restaurant on 23 May.
It was revealed in November that Ms Coladangelo had been given a role as a non-executive director at the Department of Health and Social Care (DHSC), despite there being no public record of the appointment.