A small part of a seven-storey residential block in Hardwicks Square has been damaged in a blaze.
The child left the building before firefighters arrived while an adult was rescued by crews via an internal staircase.
The fire is believed to have been accidental and caused by cooking.
LFB says cooking with hot oil can be really dangerous and the risk increases when you start frying food more than once.
A London Fire Brigade spokesperson said: “Cooking should never be left unattended on the hob or grill – if you have to leave the kitchen, turn off the heat.
“Be fabric aware – loose clothing can easily catch fire, so take care not to lean over a hot hob, and always keep tea towels and cloths away from the cooker and hob.
“Cooking with hot oil can be really dangerous and the risk increases when you start frying food more than once. All it can take is for you to become distracted for a few seconds and your cooking oil can quickly go up in flames.
“Never fill a pan more than one third full of fat or oil and make sure food is dry before putting it in hot oil – oil and water are a dangerous mix.
“If the oil starts to smoke, it’s too hot so turn off the heat and leave it to cool. We also advise using an electronic deep fat fryer if possible – they have automatic temperature controls and are much safer.
“It’s also really important to keep the hob, cooker hood and extractor fan clean too – built up fat and grease can ignite and cause a fire.”
