The fire occurred near the junction of Penrhyn Road and Grove Crescent on October 23.
Three residents managed to escape unscathed before emergency services arrived at 9.45am.
The fire was successfully extinguished by 10.25am and was tackled by around 25 firefighters and four fire engines.
Crews from Kingston, Surbiton and New Malden were assisted by Surrey Fire & Rescue Service.
Authorities are currently investigating the cause of the fire.
A spokesperson for London Fire Brigade said: “Four fire engines and around 25 firefighters tackled a fire near the junction of Penrhyn Road and Grove Crescent in Kingston.
“Part of a ground floor flat in a four-storey block was damaged by fire.
“Three people left the building before firefighters arrived. There were no reports of any injuries.
“The Brigade was called at 0945 and the fire was extinguished by 1025.
“Crews from Kingston, Surbiton and New Malden fire stations attended the scene, along with a crew from Surrey Fire & Rescue Service.
“The cause of the fire is under investigation.”