Surrounding properties have been evacuated after firefighters were called to Tolworth Rise South, Kingston, just before 5am on Tuesday.
One man and another victim, were pronounced dead at the scene.
Five more men suffering from smoke inhalation were taken to a west London hospital by paramedics.
The fire was under control by 07:44 and the cause of the blaze is under investigation.
London Fire Brigade said the roof and first-floor flats were alight.
A London Ambulance Service spokesperson added: “We sent four ambulance crews, our hazardous area response team and an incident response officer.
“We assessed five patients and took them to hospital. Sadly, two people were dead at the scene.”
The roof and first-floor flats were alight, London Fire Brigade said
Eight fire engines from New Malden, Surbiton, Sutton, Wimbledon, Kingston and other nearby stations attended.
Five people in neighbouring properties have been evacuated and given temporary accommodation by Kingston Council.
The council said it is working closely with the fire brigade and the police.
Tolworth Rise South is a service road running parallel to the southbound A3.
It is closed between Southwood Drive and Oakdene Drive, Transport for London said.