A man, woman and two kids left the flat before the fire brigade arrived at the scene in London Road on Saturday at around 6.55pm.
They were treated at the scene for smoke inhalation by ambulance crews.
A flat on the third floor of the four-storey block was damaged by the fire.
The cause of the fire is believed to be accidental and involved a candle.
A London Fire Brigade spokesperson said: “Candles, incense sticks and oil burners are one of the most common causes of fire.
“We’d recommend swapping traditional candles for safer flameless LED alternatives, but if you do use real candles, it’s so important to never leave them unattended.
“Always make sure that they’re held firmly in heat-resistant holders and placed on a stable surface where they won’t be knocked over.”
The Brigade was under control by 8.35pm.
Fire crews from Surbiton, Kingston, New Malden and Twickenham fire stations were at the scene.
Firefighters’ candle safety top tips:
- Make sure you put out any candles, incense and oil burners when you leave the room and especially before bed.
- Keep them away from materials that might catch fire – that’s things like curtains, furniture, clothes and hair.
- Be aware that tea lights get very hot and without proper holders can melt through plastic surfaces like a TV or bath.
- LED candles can be a great alternative – they’re safe even if you fall asleep or forget to blow them out.
A London Fire Brigade spokesperson said: “Four fire engines and around 25 firefighters were called to a flat fire on London Road in Kingston.
“A flat on the third floor of a four-storey block was damaged by the fire.
“A man, a woman and two children left the property before the Brigade arrived.
“They were treated at the scene for smoke inhalation by London Ambulance Service crews.
“The cause of the fire is believed to be accidental and involved a candle.
“The Brigade was called at 1855 and the fire was under control by 2035.
“Fire crews from Surbiton, Kingston, New Malden and Twickenham fire stations were at the scene.”