Four fire engines put out a fire at a matzah bakery in Stamford Hill in the early hours of Wednesday.
The London Fire Brigade said 25 firefighters went to the site of "a school building" in Bethune Road.
But a spokesman for the school said the fire had occurred not at the school but "next door at the synagogue in the matzah bakery".
According to the fire service, the blaze was "believed to be accidental and caused by logs stored next to a bread oven igniting".