Police were called by the London Fire Brigade at approximately 11.06pm on Wednesday, 14 July to a fire on South Gipsy Road, Welling.
Officers and the London Fire Brigade (LFB) attended and the fire was extinguished at approximately 00:30hrs.
The cause of the fire is being treated as arson.
There were no injuries. No arrests have been made and enquiries continue.
Police are urging anyone who has information that could assist police to make contact.
Detective Sergeant Danny Banks, from the Serious and Complex Investigations Unit, said: “The victims in this incident are prominent on social media and have suffered a hugely distressing ordeal, not least because they have lost their home but have also since suffered baseless allegations on social media that they are responsible for this incident. I am happy to state that they are not and remain supportive of our investigation.
“We ask that anyone with information relating to the incident calls police on 101 or tweets @MetCC quoting CAD 8350/14July. It is vital we hear from you.”
To remain anonymous call Crimestoppers on 0800 555 111 or visit Crimestoppers_uk.org.