The victims were upstairs when they woke to the smell of smoke.
They went downstairs to find their front door on fire, and then called the emergency services. They sustained no injuries
The fire caused significant damage to the front of the property.
LFB fire crews quickly responded to the incident and the cause of the fire appeared to be a deliberate act as an accelerant had apparently been put through the letterbox.
Det. Con. Samantha Oram, attached to Lewisham CID, said: “We would like to speak to two suspects who were seen running from the location towards Mayow Road at 03:20hrs. “Both are males and of slim build.
“We believe this was a completely unprovoked attack, in which, luckily, there were no injuries.
“I would urge anyone with information to come forward and contact the investigating team on 101 quoting ref CAD 1942/01jan or provide information anonymously through Crimestoppers on 0800 555 111.”
No arrests have been made and enquiries continue. (Source: Metropolitan Police press release)