A charred shell is almost all that remains of the partially-collapsed development in Worcester Park, Sutton.
The London Ambulance Service said no injuries had been reported.
Richard Bee, a deacon at Worcester Park Baptist Church, told Premier some members of the church live near where the fire happened and were up since the early hours providing help.
"We're in the process of working with the council to work out what the best response we can offer is.
"They've been deluged by donations from the local community and have started putting up their hands and saying, 'please don't bring us any more stuff until we until we know what we actually need.' "
Church members are helping the council sort through the donations. Some members have also offered spare rooms for those with accommodation needs.
He said their aim to meet practical and spiritual needs in the situation.
"There is a space for bringing the hope of the gospel into it. But also, we need to be really careful that we're not conflating two different things. There's a very real practical need which we can meet in the immediate term. Then following that, there's a very real spiritual need which we can meet."
Resident Stephen Nobrega, a father of three children aged between eight months and 13 years old, told the PA News Agency he had "lost everything" after his ground-floor flat was destroyed.
He said: "I was woken up by my missus at about 1.20am, screaming and shouting: 'Fire! Fire!'
"I heard a lot of residents outside and by that point somebody was already banging on my window and pressing my buzzer, so I knew it was quite serious.
"Within about 20 minutes, fairly quick, it started ripping through, going from apartment to apartment, right to left, and then it started going down and caught alight on the other side."
By dawn, crews were still present pumping water into the blackened building, as a thick plume of acrid smoke drifted across the parkland towards Morden cemetery.
The cause is not yet known.
Bee has encouraged Christians to support through prayer.
"We can be praying for primarily for the people who've lost their homes," he said.
"It might just be stuff, but stuff is precious to us. Homes are precious to us. This can be a lot of disruption. I think we can be praying for the people who have the emotional difficulty of looking at burned out wreck of a building that used to be their home and wondering what life can look like as a result of that."
The cause of the fire is not yet known.
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