The London Fire Brigade said a single-storey building at the back of a shop was completely destroyed by the fire.
Three men were rescued from the building by fire crews wearing breathing apparatus, said the Brigade.
They were treated at the scene by London Ambulance crews and the Helicopter Emergency Medical Service. All three of the men have been taken to hospital.
The Brigade asked members of the public to avoid Hoe Street as well as nearby Forest Road at the junction with Hawthorne Road.
Fire crews from Walthamstow, Leyton, Tottenham, Woodford, Homerton and Bethnal Green fire stations were called to the scene.
The cause of the fire is being investigated by the Brigade and the Metropolitan Police Service.