The Health Secretary bashed lockdown adviser Neil Ferguson after he allowed the woman to visit him at home while lecturing the public on the need for strict social distancing.
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The 51-year-old has now quit his government advisory role after The Telegraph revealed he allowed married Antonia Staats to come over.
This morning Mr Hancock said he made the right call to resign.
He told Sky News: “He took the right decision to resign.
“Its’ extraordinary. I don’t understand.
Presenter Kay Burley asked him if he was speechless.
He replied: “That doesn’t often happen to me, I am.
“Professor Ferguson is a very eminent and impressive scientist. The science he has done has been an important part of what we have listened to.
“I think he took the right decision to resign.”
And he even admitted he would back the cops if they chose to fine him.
He added: “It’s a matter for the police.
“I think the social distancing rules are very important and people should follow them.
“Absolutely, I back the Scottish police, the English police… They will take their decisions independently of ministers.”
And Security Minister James Brokenshire insisted he had to go.
He said: “Professor Ferguson has obviously made his statement, underlined there is no excuse not for following the social distancing rules and I think he’s made the right decision here.
“If you look at what he said he was wrong to take the action he did, as he said in his statement.”
Mr Brokenshire also dismissed he academics defence that he thought he was immune because he’d had the virus.
He added: “I think it’s still far too early with this new and novel disease to be able to make these sorts of judgements, which is why Professor Ferguson has taken the decision he has.”
Ms Staats, 38, lives with her husband and their children in a £1.9million house.
They are understood to be in an open marriage.
Professor Ferguson leads the team at Imperial College London that handed a bombshell piece of research to the government that said failing to take drastic action would cause 250,000 deaths and overwhelm the NHS.
Just last week he warned lifting the lockdown too early could risk an additional 100,000 deaths.
On at least two occasions, Ms Staats travelled across London to see the government scientist.
Her first visit, on March 30, coincided with a public warning by Prof Ferguson the lockdown measures would need to stay in place until June.
She made a second trip on April 8 despite telling friends she suspected her husband – an academic in his thirties – had coronavirus symptoms.
Prof Ferguson accepted he had made an “error of judgement and took the wrong course of action”.
He said: “I acted in the belief that I was immune, having tested positive for coronavirus, and completely isolated myself for almost two weeks after developing symptoms.
“I deeply regret any undermining of the clear messages around the continued need for social distancing to control this devastating epidemic.
“The Government guidance is unequivocal, and is there to protect all of us.”
A Government spokesman confirmed Prof Ferguson had stepped back from his role.
She declined to comment.