Four fire engines and around 25 firefighters attended a fire at a flat on Copperfield Road in Mile End.
Part of a kitchen in a second-floor flat was damaged by fire. One woman and one child left the flat before firefighters arrived and there were no reports of any injuries.
The fire is being treated as accidental and believed to have been caused by cooking left unattended.
A London Fire Brigade spokesperson said: "Fires are more likely to start in the kitchen than any other room in the home. If you have to leave the kitchen, turn off the heat and never leave cooking unattended.
"You can keep safe by following our simple cooking tips such as never placing anything that can catch fire near the hob. Keep all objects, like tea towels, cloths, plastic bowls and anything flammable well away from the cooker and always check the hob is turned off when you've finished cooking.
"Attempting to extinguish a fire by yourself can lead to injuries or even be fatal and can increase the risk of more severe damage to your property. Leave the room, close the door, shout a warning to others and call 999."
The Brigade was called at 1250 and Control Officers mobilised crews from Millwall, Shadwell, Plaistow and Stratford fire stations to the scene. The fire was extinguished by 1326.