During a visit to Birstall in West Yorkshire ahead of this week's Batley and Spen by-election, the PM was pressed over the scandal which saw Mr Hancock resign on Saturday after pictures emerged showing him kissing an aide he had appointed to the Department for Health and Social Care.
After the images emerged on Thursday night, Mr Hancock bowed to pressure on Saturday afternoon and quit after CCTV emerged of him breaking social distancing guidelines to combat Covid-19 by intimately embracing aide Gina Coladangelo.
The long-term friend of Mr Hancock was brought into the Department of Health and Social Care (DHSC) first as an unpaid adviser before getting the £15,000-a-year role of non-executive director in September.
Asked if he regretted backing Mr Hancock on Friday when he resigned Saturday, Mr Johnson said: "I read the story on Friday and by Saturday we had a new secretary of state for health and I think that’s about the right pace to do things given that we’ve got a national pandemic.
"I had a long conversation with [new Health Secretary] Sajid Javid yesterday in which we had a very careful look at the data with colleagues and we assessed where we were."
The PM, who visited PPG Architectural Coatings in Birstall, spoke about Covid data and lockdown lifting, adding: "With every day that goes by we’re more and more convinced that July 19 will be the terminus date and that we’ll be able to get back to something like a life as it was before Covid."
Asked a second time about Mr Hancock's potential future in public life, he said again: "I read the story on Friday and we had a new Health Secretary on Saturday and I think Sajid Javid will do an outstanding job."
And pushed third time on reports that a complaint has been registered with the police over Mr Hancock’s breach of social distancing rules, the PMsaid: ” Obviously that’s an operational matter for the police, not something you’d expect me to comment on but I think the crucial thing for the public for everybody is that I saw the story on Friday notwithstanding the difficulties the country faces during a pandemic, we had a new secretary of state for health on the Saturday.”
Mr Johnson also would not comment when asked if he had ever used his personal email address to conduct Government business.
It comes as Labour demanded an investigation into allegations that Matt Hancock and junior health minister Lord Bethell used their personal accounts for business in Government.
The Prime Minister told reporters: "I don't comment on how I conduct Government business. But I can tell you that we in this Government are getting on with focusing on the people's priorities."
Earlier, the Justice Secretary insisted "due process" was followed in appointing the aide Matt Hancock was caught kissing to a paid role at the health department.
Robert Buckland told Sky News: "Everything that I understand so far leads me to believe due process was followed in the appointment of this person and any declarations that should've been made were made."
But pressed on when Mr Hancock's relationship began with the aide, the Justice Secretary said: "I'm confident that due process was followed and that declarations were made; as to when the relationship began, I'm afraid I don't know."
Mr Hancock's replacement as Health Secretary, former chancellor Sajid Javid, said the camera that caught the embrace has been disabled and suggested its presence would be investigated.
Mr Johnson initially stuck by Mr Hancock after the Sun published footage on Friday of him kissing the aide, an old friend from his days at Oxford University, in his ministerial office on May 6.
The scandal led to renewed questions over standards in Mr Johnson's Government after a series of controversies surrounding some of his most senior ministers.
Mr Johnson rejected calls to fire Home Secretary Priti Patel when she was found to have bullied civil servants working for her, while Housing Secretary Robert Jenrick conceded that his approval of a major property development involving Tory Party donor Richard Desmond was "unlawful".