Parents had argued that Downhills Primary was now thriving - and that turning it into an academy made no sense.
But, as he refused permission for a judicial review, Mr Justice Kenneth Parker said that it was a rational decision to turn it into an academy, in the light of the school's "egregious" past performance.
He said that it was clear that the Education Secretary "simply had no confidence" that the school would substantially improve if it remained within the control of Haringey Council.
On the other hand, he "believed firmly" that conversion to an academy would substantially improve performance.
More top news
Sadiq Khan says he wants a "common sense solution" to keep Fabric nightclub open, after the drug-related deaths of two teenage boys.
A man who died from a single punch during a night out texted his girlfriend just two hours before he was attacked telling her he loved her.
Do you know how many steps you would have to take to walk between Oxford Circus and Bond Street stations? Well wonder no more.