Cummings made the accusation in an explosive blog post that exceeds 7,000 words, the latest in a series of stinging attacks he has made on the prime minister since leaving Number 10.
The blog included WhatsApp messages that Cummings said are from the prime minister, describing health secretary Matt Hancock as "totally f***ing hopeless".
Describing Johnson's conduct in crucial meetings, Cummings wrote: "The PM who as soon as things get ‘a bit embarrassing’ does the whole ‘let’s take it offline’ shtick before shouting ‘forward to victory’, doing a thumbs-up and pegging it out of the room before anybody can disagree.”
The blog post is the latest salvo in a bitter row between the former aide, the prime minister, and Hancock, who Cummings has singled out for much of the blame for failings during the COVID crisis.
Cummings said messages he published today show that “No10/Hancock have repeatedly lied about the failures last year” and accused them of now trying to “rewrite history”.
Watch: Boris Johnson allegedly called Matt Hancock 'hopeless'
Cummings, who left Downing Street in November during a power struggle, accused the prime minister of now publicly supporting the “fiction” that he has been in agreement with the health secretary throughout the pandemic.
The former chief aide argued the messages show otherwise, as do Johnson’s moves to carve up some of Hancock’s responsibilities and hand them to other individuals.
In one exchange on 3 March last year, Cummings highlighted the US’s rapid increase of testing capacity and criticised Hancock for saying he was “sceptical” about meeting a new UK target having earlier said it would “definitely” be met.
Johnson apparently responded: “Totally f****** hopeless.”
Cummings also published another exchange about the struggles to procure ventilators for COVID patients, saying officials were turning down equipment because of price hikes.
“It’s Hancock. He has been hopeless,” the contact appearing to be Johnson replied on 27 March last year.
Downing Street has previously suggested that Cummings may be in breach of the code of conduct for special advisers if he releases government information.
A No 10 spokesman said: “We expect all current and former special advisers to act in full accordance with that code of conduct.”
Cummings has been highly critical of the prime minister, and made a series of explosive claims when questioned by MPs last month.
He claimed that Johnson described the looming pandemic last year as a “scare story”, and that he ignored advice from Chris Whitty and Sir Patrick Vallance over the need to implement a two-week lockdown in September.
Cummings also accused the health secretary of lying, failing on care homes and “criminal, disgraceful behaviour” on testing.
Hancock has denied the allegations and said last week it was “telling” that Cummings was yet to provide the joint Health and Social Care Committee and Science and Technology Committee with written evidence.
The health secretary said he had “no idea” why Cummings had a dispute with him, while No 10 has said the prime minister has confidence in Hancock.
The prime minister previously rejected Cummings’ claims, telling MPs that “some of the commentary I have heard doesn’t bear any relation to reality”.
Johnson denied Cummings’s charge that government failings had resulted in tens of thousands of unnecessary deaths.
Asked whether those deaths were due to his “action or inaction”, Johnson said: “No, I don’t think so.
“Of course this has been an incredibly difficult series of decisions, none of which we have taken lightly.”
Watch: Starmer: Cummings was 'absolutely right' about PM