On Friday, Mr Johnson received a questionnaire as part of the police inquiry into allegations of lockdown-busting gatherings held in Downing Street. 

Anyone found to have breached the law risks receiving a fixed penalty notice. Sir Iain Duncan Smith, the former Tory leader, said on Friday that it would be “very tough” for Mr Johnson to remain in office if that happened.

Mr Green’s intervention came after Sir Bob Neill, the chairman of the justice select committee and another member of the One Nation group, said it was “completely inappropriate to suggest there should be any special treatment for anyone involved in these inquiries”.

Sir Bob described any “political pressure on the police” as “completely reprehensible”.

But Number 10 distanced itself from the remarks seen as putting pressure on officers, with a spokesman saying: “This government has always backed the police and fully respects their complete independence to carry out inquiries without fear or favour.”

Some 50 government figures are being sent formal questionnaires as part of Operation Hillman. They will have seven days to respond to the allegations of illegal behaviour.

Speaking before her resignation, Dame Cressida Dick, the Metropolitan Police Commissioner, said: “Clearly some but probably not all of those people may very well end up with a fixed penalty notice. I recognise this is something that has hugely disgusted many members of the public to see. It has caused lots and lots of public concern.”