Ten fire engines and around 70 firefighters were called to a fire on Hall Lane in Chingford.
Firefighters tackled a fire at an end of terrace shop with flats above, parts of the ground floor and first floor were damaged by fire. The roof and an internal staircase were significantly damaged and have partially collapsed.
One woman and one child left the building before the Brigade arrived and were taken to hospital by London Ambulance crews.
Road closures will remain in place for the next few hours and residents are advised to avoid the area due to significant traffic disruption.
The Brigade's Control Office was first called at 1135 and fire crews from Walthamstow, Chingford, Tottenham and other surrounding fire stations attended the scene. The fire was brought under control at 1349.
The cause of the fire will be investigated by the Brigade's Fire Investigation Unit.