Boris Johnson’s former top adviser said the plan had been to develop resistance in the population in the months leading up to September.
Mr Cummings claimed the idea was only abandoned in early March after Downing Street was warned that it would lead to a “catastrophe”.
He tweeted: “Media generally abysmal on Covid but even I’ve been surprised by one thing: how many hacks have parroted Hancock’s line that ‘herd immunity wasn’t the plan’ when ‘herd immunity by September’ was ‘literally the official plan in all documents/graphs/meetings’ until it was ditched.
“In week of March 9, No10 was made aware by various people that the official plan would lead to catastrophe.
"It was then replaced by Plan B. But how ‘herd immunity by September’ could have been the plan until that week is a fundamental issue in the whole disaster.”
Mr Cummings also claimed there had been “so much lock down confusion”.
He added: “Obviously they’re ‘destructive’. But if you have to do it because alternative is ‘hundreds of thousands choking to death and no NHS for months for everybody else and economy sunk because everybody hiding in terror’ then earlier/harder is better for health AND economy.
“If we’d had the right preparations and competent people in charge, we would probably have avoided lockdown 1, ‘definitely’ no need for lockdowns 2 and 3.
“Given the plan was AWOL/disaster and awful decisions delayed everything, lockdown 1 became necessary.”
His intervention comes as he prepares to give evidence on Wednesday to MPs on the Commons health and science committees who are investigating the Government’s response to the pandemic.
SNP MP and Science and Technology committee member Carol Monaghan has now demanded answers.
She said: "It is an unedifying sight to see the architects of the Vote Leave government go at loggerheads over their decisions that cost lives throughout this pandemic.
"However, Boris Johnson has some serious questions to answer as to why he delayed going into lockdown and why his hesitancy to close the borders off to new variants.
"We are currently seeing the consequences of Boris Johnson dithering on closing the borders as new variants are putting our progress at risk."
The Home Secretary Priti Patel denied the claims, saying it was "absolutely not" true.
She told the BBC’s Andrew Marr show: “Our strategy was always about protecting public health, saving lives and protecting the NHS.
“Absolutely all colleagues involved in those meetings and discussions, working with the chief scientist and the chief medical officers, absolutely recognised that from the very difficult discussions that we had.
“At the time of a crisis when government is making very, very tough decisions, difficult decisions, we put public life and protecting the public at the forefront of all those decisions.”
It was also denied by the chief executive of the UK Health Security Agency.
Dr Jenny Harries said: “I can categorically say I have never been in any Government meeting where herd immunity was put forward at that point of the pandemic as a mechanism of control.”