Fire crews faced an “intense blaze” throughout the whole of the ground floor of the property, the LFB said.
Four young children were taken out of the house and given CPR by firefighters at the scene before being taken to hospital where they died.
The fire was under control by 8.36pm and the cause is under investigation.
London Fire Commissioner Andy Roe said: “This is an incident that has left everyone numb with profound sadness. My thoughts are with the family and friends of the children, the whole local community and all those who will be affected by this fire.
“Fire crews arrived quickly and located the children inside the property.
“They were brought out of the house and given immediate emergency care. The welfare of our staff involved in this incident is very important to us and all of them will be offered counselling as a priority.”