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The health secretary said he was left “speechless” after The Daily Telegraph reported that Ferguson, who has played a key role in advising the government, allowed a woman to visit him at home in London on at least two occasions during the lockdown.
Hancock told Sky News on Wednesday morning that Ferguson had made the “right decision to resign” from the Scientific Advisory Group for Emergencies (Sage).
Asked if Ferguson should be prosecuted, Hancock said it was “a matter for the police”.
“They will take their decisions independently from ministers, that’s quite right, it’s always been like that,” he said.
“Even though I have got a clear answer to what I think, as a minister the way we run the police is that they make decisions like this.
“So I give them their space to make that decision, but I think he took the right decision to resign.”
Hancock said Ferguson’s actions were “extraordinary” and it was “just not possible” for him to continue advising the government.
He added that the social distancing rules “are there for everyone, they are incredibly important and they are deadly serious”.
“They are the means by which we have managed to get control of this virus.”
Ferguson has said that he regretted “undermining” the continued need for social distancing to tackle coronavirus.
Ferguson’s research with Imperial College London colleagues warned that 250,000 people could die in the UK without drastic action before Boris Johnson imposed the restrictions.
“I accept I made an error of judgment and took the wrong course of action. I have therefore stepped back from my involvement in Sage,” Ferguson said in a statement.
“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.”