UK prime minister Boris Johnson referred to the inability of his health secretary, Matt Hancock, to increase coronavirus testing capacity at the start of the pandemic as “totally fucking hopeless”, according to private messages disclosed by his former top adviser.

Dominic Cummings released the damaging WhatsApp messages on his blog on Wednesday. They show that Johnson considered sacking Hancock in a message he sent to his former aide on April 27 2020, revealing that he thought the provision of personal protective equipment was “a disaster”.

Johnson added in the message: “I can’t think of anything except taking Hancock off and putting [Michael] Gove on.”

The comments undermine Downing Street’s insistence that “the prime minister has full confidence in the health secretary”, showing Johnson’s own doubts about the abilities of Hancock during the health crisis.

Downing Street on Wednesday said: “[No 10] does not plan to engage with every allegation made. The PM has set out that we’ll hold an official inquiry next year . . . our focus is on recovery from the pandemic,” adding that Johnson had full confidence in Hancock.

“The PM has worked very closely with the health secretary throughout this pandemic and will continue to do so,” said No 10.

In his blog post, Cummings said Johnson had a “clear plan to leave at the latest a couple of years after the next election”, adding “he wants to make money and have fun not ‘go on and on’.” No 10 dismissed the claims as “utter nonsense”.

In May, Cummings revealed in parliamentary testimony that he had repeatedly demanded Hancock’s sacking for failings and “lies” at the start of the pandemic. Hancock has denied ever telling any untruths to Johnson.

A second WhatsApp exchange from March 27 2020 showed Cummings complaining that the health department had turned down ventilators on price grounds. Johnson replied: “It’s Hancock. He has been hopeless.”

The third exchange occurred on the same date showing Cummings complaining that the US had gone from 2,200 tests a day to 27,000 to 100,000 in just a fortnight. Hancock, by contrast, was “sceptical” about the UK reaching 10,000 daily tests by the following week, according to Cummings.

Johnson replied: “Totally fucking hopeless.”

Hancock eventually set a target of 100,000 daily tests in early April, which was met a month later.

Britain’s lack of testing capacity at the start of the crisis has been a focus of criticism of the government.

One of Cummings’ most damaging claims was his suggestion that Hancock reassured Johnson that all people moved from hospitals to care homes would be tested beforehand, which did not happen. Hancock has defended himself, insisting that testing was done when there was sufficient capacity.

Cummings said in his blog that Downing Street forced Hancock to create the more ambitious testing plan of 100,000 daily tests.

“Hancock is creating a new version of reality in which he came up with the idea to ramp up testing before 14 March,” he wrote, adding: “The reality: as part of the transition to Plan B, No10 forced a new testing plan on Hancock, who was still operating under Plan A / herd immunity assumptions in the week of 16/3 according to which community testing was pointless.”

The former aide last month accused Johnson of presiding over a chaotic and unprofessional pandemic response which had led to tens of thousands of unnecessary deaths.

In his blog, he wrote: “If No10 is prepared to lie so deeply and widely about such vital issues of life and death last year, it cannot be trusted now either on Covid or any other crucial issue of war and peace.”

Hancock announced this week that the lifting of lockdown measures would be pushed back to July 19 to enable the NHS to inoculate all over-fifties, healthcare workers and the most vulnerable.

Speaking at prime minister’s questions, Labour leader Keir Starmer argued that Johnson’s “indecision” on placing India on the red travel list had prompted the UK-wide spread of the Delta variant first identified in India.

“The British people did their bit, by following the rules and getting vaccinated. But the prime minister squandered it by letting a new variant into the country”, he said.

Public health advisers warned earlier on Wednesday that the spread of the Delta variant had accelerated the number of new infections and hospitalisations in the UK.

“What we are seeing at the moment are about 7,000 to 8,000 infections per day . . . But we know that is less than half of what the true infections are in the community”, Susan Hopkins, deputy director at Public Health England’s National Infection Service, told MPs at a select committee.

She added that without vaccination or social restrictions, the reproductive number could rise to 7 across the country, meaning that for every 10 people with coronavirus, a further 70 would be infected.