The Brexit campaign promise to give the NHS an extra £350 million per week if the UK left the European Union “drove everyone crazy” because it was true, according to Dominic Cummings.

The former Vote Leave mastermind admitted the figure, which was emblazoned on campaign buses used by key Brexiteers such as Boris Johnson, was used as a “trap” for the Remain side as it exposed the “true balance sheet” of EU membership.

Critics have argued the figure was misleading as it did not take into account the rebate the UK received from Brussels.

But in an interview with the BBC, Mr Cummings said: “The reason why that figure worked and the reason why it drove everyone crazy and the reason why people are still talking about it now is that we were using true figures.”

In a candid admission, he also said it was “perfectly reasonable” to argue that Brexit was a mistake, but that anyone who was confident either way had “got a screw loose”.

I think that the way in which the world has worked out since 2016 vindicates the arguments that Vote Leave made in all sorts of ways

The former Downing Street aide said he thought Brexit was a “good thing” based on events of the past five years.

“I think it’s perfectly reasonable to say Brexit was a mistake…of course it’s reasonable for some people to think that,” he continued.

“I think that obviously I think Brexit was a good thing… I think that the way in which the world has worked out since 2016 vindicates the arguments that Vote Leave made in all sorts of ways. I think it’s good that Brexit happened.”

Mr Cummings revealed during the hour-long programme that he had helped broker a deal between Boris Johnson and Michael Gove to head up a new government after the Brexit result.

Asked whether he thought Mr Johnson would become the next prime minister after the shock 2016 poll, Mr Cummings, who worked with Mr Gove when he was education secretary, said: “Yeah, sort of.

“I thought that, so I negotiated between him and Michael Gove a deal over the previous couple of weeks about what to do in this situation.

“The deal actually was that Michael did not want to run in the leadership contest, that he would be chancellor, that Boris would be prime minister, but that we would create a certain kind of Number 10, and that we would very rapidly deliver all the promises that the campaign had made during the referendum campaign.”

While the programme was aired, Mr Cummings also took questions on Substack, where subscribers pay to read his views since he left Government in the autumn following a power struggle in No 10.

Pressed on what his reaction was when Mr Gove “blew up the deal you had brokered”, he replied: “Cross. I’d promised my wife not to get involved with the leadership campaign so got a very big surprise (when) it all fell apart in about five days.”

Explaining his rationale for agreeing to the wide-ranging discussion, Mr Cummings said he agreed to an interview with BBC political editor Laura Kuenssberg “in early 2016” and that he “had to keep the promise”.