The Save Downhills campaign group said they were "disappointed but not surprised" their application was refused and were considering whether to appeal.
The group said in a statement: "Today's ruling shows that consultation during academy conversion is irrelevant.
"Parents' voices have been completely ignored. The law appears constructed to ensure that only one man, the Secretary of State, can make decisions about any school's future. Downhills is a happy, inclusive and improving school as the latest test results and Ofsted monitoring will show.
"We believe we are the victims of his wider political agenda. He publicly abused us as 'enemies of promise' and said he was 'marching towards the sound of gunfire'. We continue to believe Mr Gove has abused his power, denying parents and local communities their legitimate voice."
More top news
Police in Greenwich are trying to identify a man after an assault on an elderly woman in Plumstead.
Relatives of those killed in the Hyde Park attack 35 years ago marched in central London to bring an accused bomber to justice.
A new system will allow authorities to track private drones as research finds the heavier flying gadgets could smash plane windscreens.