London Fire Brigade advised people living near the fire on West Mews to keep doors and windows closed as a precaution because of smoke.
A spokesman said firefighters "don't believe" anyone was inside the burning building.
At one stage crews were using jets to protect a 2,000-litre diesel fuel tank. The cause of the blaze is not known.
The front of the building, a single-storey unit, has partially collapsed.
Four people from a nearby building were initially unaccounted for but were located by firefighters.
London Fire Brigade said it was called at around 18:20 BST to the incident. Ten engines and 72 firefighters and officers are at the scene.
From there station manager Charles Hanks said: "Crews were confronted with a large fire when they arrived and are now working hard to confine it to the bakery and stop it from spreading to any neighbouring factory units.
"There is some fuel stored on site but crews have isolated the supply and it is not involved in the fire."
He added: "The fire is producing a lot of smoke so we are advising residents to keep their doors and windows closed as a precaution while it is going on. Thankfully though no injuries have been reported."
More than 70 firefighters are dealing with a blaze at an industrial bakery unit in Tottenham.