Dominic Cummings told a parliamentary committee Hancock "should have been fired for at least 15, 20 things including lying to everybody in multiple occasions in meeting after meeting in the cabinet room and publicly."
Asked for an example, Cummings said Hancock had said that all patients got the treatment they needed during the first peak of the virus.
Cummings said that was contrary to briefings from the government's health experts, who had said some patients had not received necessary treatment.
He also said Hancock had told ministers that the supply of personal protective equipment was under control in April, but that had later proved not been the case.
Cummings also said the country's top civil servant had told him he had lost confidence in Hancock's honesty.
Neither Hancock's department or his adviser immediately commented.