Dominic Cummings has been criticised by a watchdog for failing to seek approval before setting up his paid-for blog, which he uses to make revelations about his time as the prime minister’s chief adviser.

Cummings, who was ordered by Boris Johnson to leave Downing Street in November, has applied to undertake consultancy work, according to correspondence from the Advisory Committee on Business Appointments (Acoba).

Details of the work and for whom were redacted in correspondence between Acoba and the Cabinet Office. It was published online after Cummings made his application.

The watchdog also published a letter to Cummings – sent in June by its chair, Lord Pickles – which said it was unclear whether the application related to work other than his Substack blog, which subscribers pay £10 a month to read.

The letter, which cited a report in the Times saying that Substack “offered a profitable platform” for him, added that the committee did not appear to have received, or advised him on, an application in relation to the blog.

Former ministers and officials must apply for advice from Acoba when they take up any new paid or unpaid appointment outside government within two years of leaving office.

“The government’s Business Appointment Rules exist to protect the integrity of government; and make it clear that new appointments/employment should not be taken up or announced before receiving advice. It appears you may be in breach of these rules,” added the letter, which said the committee was seeking clarification.

A letter on 10 September to the Cabinet Office from Cat Marshall, the committee secretariat, said: “This failure to seek and await the committee’s advice was a breach of the rules reported to the Cabinet Office in July.”

It added: “Mr Cummings has not provided the committee with a response to its correspondence in respect of the breach of the rules.

“This application to consult for [redacted] relates directly to his previous breach of the rules and as a consequence the committee refuses to provide advice on this occasion.”

In June, Cummings launched a profile on Substack, a platform that allows people to sign up to newsletter mailing lists.

In a post on the site, he said he would be giving out information on the coronavirus pandemic for free, as well as some details of his time at Downing Street.

He added that revelations about “more recondite stuff on the media, Westminster, ‘inside No 10’, how did we get Brexit done in 2019, the 2019 election etc” would be available only to those who paid the £10 a month for a subscription.