The infamous Vote Leave slogan, painted on the side of a bright red bus, quickly became a symbol of all that was wrong with the Brexit referendum campaign.
A decision to issue a summons was made by a district judge in May for Johnson to attend Westminster Magistrates’ Court to face three allegations of misconduct in public office.
But the decision was ruled “unlawful” and quashed by High Court judges at a hearing in June.
Ball’s legal team filed an application for permission to appeal to the Supreme Court over the ruling.
However, the application was thrown out on Wednesday by Lady Justice Rafferty – one of the High Court judges who quashed the original decision.
In a brief announcement, she said: “This application for leave to appeal to the Supreme Court is rejected.”
Ball now has the option to apply directly to the Supreme Court for permission, the Press Association reports.
Speaking outside court after the ruling, he said: “This isn’t over, we are not giving up.
“We are pursuing it, absolutely.”
The £350 million figure was emblazoned on the red campaign bus used by Vote Leave during the referendum, with the slogan saying “We send the EU £350 million a week, let’s fund our NHS instead”.
Giving reasons for the High Court’s ruling in July, Lady Justice Rafferty said the “problem of false statements in the course of political campaigning is not new” and that Parliament had enacted laws to deal with “certain false campaign statements which it considers an illegal practice”.
However, she said this did not include false statements relating to publicly available statistics, and found that the district judge’s decision would have “extended the scope” of the offence of misconduct in a public office.
She also said it appeared that “there would have been no complaint” if Mr Johnson had used a figure of “£350 million per week gross, or £250 million per week net”.