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
A woman hit by police gunfire during a counter-terrorism operation has been arrested after being released from hospital.
Police have been granted extra time to question a man who is being held on suspicion of planning a terror attack.
Joshua beat the older, more experienced boxer in front of 90,000 fans in Wembley Stadium.