Residents have been living in hotels since the blaze destroyed the fourth floor and roof of Fox House, on Maysoule Road, in Battersea, on September 10.
Wandsworth Council, which owns the block, confirmed it has now offered most secure tenants permanent homes elsewhere in the borough, as the building remains unsafe to access.
The authority hopes to have rehomed all residents by the end of the month.
Around 100 firefighters rushed to the scene after the blaze was reported at 7.09pm on September 10.
They evacuated roughly 150 residents from the five-storey building and got the fire under control by 11.01pm.
No injuries were reported.
Residents told the Local Democracy Reporting Service (LDRS) the next morning they feared they had lost everything in the blaze, as they anxiously waited to find out more about the extent of the damage, if they could retrieve their belongings and what would happen next.
Isabel Lubeiro, 59, and her son Alex Langley-Lubeiro, 27, said they believed their home, where they had lived for 26 years, had suffered major smoke and water damage as it sat directly below the top floor where the fire started.
They said they believed they had lost most of their possessions due to the blaze.
“The smoke destroys everything,” Isabel told the LDRS. “We’ve probably lost everything.”
Councillors and officers acknowledged the devastation caused by the incident at a meeting of the Housing Committee on October 2.
They said the council had acted quickly to provide immediate support to residents, including vouchers, and was prioritising permanently rehousing them.
Labour councillor Sarah Davies said: “I just feel so very, very sorry for the residents involved and I know that this is life-changing for them.”
She said she had seen “the very best of the council coming together to give them all the very personalised care and attention that they needed”.
Dave Worth, the council’s Director of Housing Services, said the authority provided temporary accommodation for roughly 31 families who needed somewhere to stay on the night of the incident, although some residents had to wait into the early hours of the morning for their placement.
He told the meeting the council had already offered permanent alternative council homes to roughly 27 of the 29 households who were living in the block under a secure lifetime tenancy, and it was supporting the other residents with rehousing.
He added officers hoped to have resettled all residents who were in temporary accommodation by the end of the month.
Mr Worth expressed his “pride and gratitude in all of the staff who turned out on the night and who have turned out since, it has been… a really good example of the council working across departments together”.
The committee heard it had been difficult to give tenants access to the building to retrieve belongings, but the council was organising getting them in safely to get their possessions.
Labour councillor Kate Stock said the support provided to residents had shown the “best of Battersea”.
She said: “I know that there is more work to do to get people settled and for them to be able to get possessions for them to continue to live their lives and to understand when and if they’re going to be able to return to Fox House.”
Councillor Stock said residents were concerned about why the fire had spread so quickly, the authority’s previous assessment of this risk and what action might be needed as there were other council blocks of a similar design on the road.
Mr Worth said the London Fire Brigade (LFB) had not been able to determine the cause of the fire as the building was still not safe enough to access.
He said the council would use LFB’s findings, when investigators could get into the block, to inform next steps.
