On March 3 last year, the controversial former aide highlighted the US’s ramping up of testing capacity and criticised Mr Hancock for saying he was “sceptical” about meeting a target.
The Prime Minister purportedly responded: “Totally ******* hopeless.”
Mr Cummings, who left Downing Street in November during a bitter power struggle in No 10, has targeted much of his criticism since leaving at the Health Secretary.
On Twitter, Mr Cummings set out questions he believed Boris Johnson should be asked about the Government’s handling of the pandemic.
He wrote: “Given his failures on testing, care homes and PPE why did you keep in post a Secretary of State you described yourself as ‘totally ******* hopeless’ and how many more people died as a result of your failure to remove him?
“Why is No10 lying, including to Parliament, about the fact that the original plan was “herd immunity by September” and had to be abandoned?
“When did Patrick Vallance brief you on NHS data showing that the death rate at the first April peak was much higher than before/after the peak and do you now agree with Hancock that every patient got the treatment they needed?
“Do you now agree with Hancock that there was no shortage of PPE or do you agree with yourself in April 2020 that PPE supply was ‘a disaster’ that required moving Hancock?
“How many people died in care homes because of what you called the ‘disaster’ on PPE and what you called Hancock’s ‘totally ******* hopeless’ performance on testing in March?
“When will the SoS come to the House and correct his many false statements to MPs?”