Police should consider whether to take further action against a scientist who admitted “undermining” social distancing rules despite being a key figure in influencing the lockdown, the Health Secretary has said.

Matt Hancock said Professor Neil Ferguson “took the right decision to resign” as a Government adviser after conceding he made an “error of judgment” by allowing a woman to visit him at home.

The Imperial College London researcher, whose work was crucial in Boris Johnson’s move to enforce strict conditions, stood down from the Scientific Advisory Group for Emergencies (Sage).

Mr Hancock said he was rendered speechless after learning of Prof Ferguson’s “extraordinary” breach of the rules.

The Cabinet minister praised him as a “very eminent” scientist whose work has been “important” in the Government’s response, but said he had to resign.

Asked about police involvement, Mr Hancock told Sky News: “They will take their decisions independently from ministers, that’s quite right, it’s always been like that.

“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.”

The Telegraph reported that Prof Ferguson allowed 38-year-old Antonia Staats, said to be his “lover”, to visit him at home in London at least twice during the lockdown, on March 30 and April 8.

Scotland Yard is yet to comment on whether officers will speak to the pair.

Prof Ferguson’s research warned that 250,000 people could die in the UK without drastic action before the Prime Minister imposed 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,” Prof Ferguson 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.”

Prof Ferguson said on March 18 that he had the fever and cough symptoms of Covid-19 and there was a small risk he had infected others in highlighting “the need for the response which has been enacted”.

Mr Hancock, who himself has overcome Covid-19, said the science is not yet conclusive as to whether surviving an infection means there is a low risk of spreading the virus.

“Everyone has got to follow the social distancing rules,” he responded, shaking his head, when asked if Prof Ferguson could return to the role if immunity was proved.

His is not the first high-profile resignation of the pandemic, with Catherine Calderwood quitting as Scotland’s chief medical officer after making two trips to her second home.

Police spoke to Dr Calderwood and issued her with a warning after the breach was made public.

Mr Hancock said: “Absolutely I back the police. I back the Scottish police and I would back the police here.”

The latest data shows more than 9,000 fines have been issued across England and Wales for flouting lockdown rules.

Prof Ferguson, a mathematician and epidemiologist, led the Imperial team that modelled the spread and impact of Covid-19 in a Government-commissioned report.

The paper said merely slowing the spread of the virus, which had at that point been the aim, would have led to the NHS being overwhelmed by cases.

Around 250,000 people could have died in the UK in that scenario but the research said stricter measures would drastically reduce this.

The Prime Minister then announced the lockdown on March 23, ordering the public to stay at home as he shut most shops and gave police unprecedented enforcement powers.

Under those measures, partners who do not live together were told they could no longer see each other.

Imperial College London said Prof Ferguson “continues to focus on his important research”.