Officials from the London Fire Brigade said the fire began on the ninth floor of Lakanal House on the Sceaux Gardens estate in Camberwell and spread rapidly to the 11th floor. Many residents had their windows open, funnelling oxygen to the flames.

Residents were asking yesterday how 30 people became trapped in the flats, which underwent a £3m refurbishment two years ago, and if escape routes and fire-prevention measures were adequate. The 12-storey block of 96 flats had one central staircase.

Carol Cooper, 38, who lives on the seventh floor, said she saw people screaming and waving for help. "Everyone was here. But it took too long for them to get in there and do something. I think that's because it's like a maze." Ed Hammond, 37, an accountant who lives on the seventh floor, described the flats as death traps. "If the fire is in the central area, you would virtually have nowhere to go," he said. "I hate it. It's the safety ? it's just not right."

Brian Coleman, chairman of the London Fire and Emergency Planning Authority, told Sky News: "In buildings such as this one you should be safe for an hour before fire jumps from floor to floor. That wasn't the case in these circumstances and I think we need to know why the fire spread so quickly and jumped between floors in such a short space of time." Once the single staircase becomes blocked, he added, "things become difficult".

London Mayor Boris Johnson told the BBC it seemed "suspicious" the fire spread so quickly. He added: "What we will also be trying to get to the bottom of is to what extent there were design failures in the block of flats."

Five of the six victims were named as Helen Udoaka, 34, and her three-week-old daughter Michelle; Dayana Francisquini, 26; Filipe Francisquini, three; and Catherine Hickman, 31. The sixth person was not named but is believed to be a four-year-old girl.

People who lived near the block expressed horror yesterday as the full extent of the blaze became apparent. The interiors of several flats were left exposed, and, on the eastern side of the building, in what appears to have been a desperate attempt at escape, bedsheets could be seen hanging tied together in a makeshift ladder.

Thirty people were rescued from the building and 15 were taken to hospital. Investigators said that all those who died lived on the 11th floor. A firefighter remains in hospital.

The Mail on Sunday reported that Mbet Udoaka, 37, raced home from work after a call from his wife, Helen, and watched helplessly as she and newborn baby Michelle died in the fire. He stayed on the phone until his wife lost consciousness, but police and firefighters would not let him enter the burning building. His cousin Mary told the newspaper: "Helen was panicking and crying, but they were on the phone to each other constantly until she was too weak to cry. He was beside himself. He so wanted to run to their rescue but was stopped."

Speaking at the scene yesterday, Chief Superintendent Wayne Chance said that officers were dealing with a "large and complex scene" and added that the "investigation is likely to take some time".

All the residents had been evacuated and many were either staying with relatives or had been housed in temporary accommodation in a nearby church hall set up by Southwark Council and the British Red Cross. The injured were taken to three London hospitals.

Nancy Kanu, 28, watched as the fire took hold after she escaped from her fifth-floor flat. "The stairs were all full of smoke," she said. "We were really scared because we couldn't walk. We were crawling through the smoke. My sister was there with her three-day-old baby who is now suffering breathing problems and I was there with my two kids."

Harriet Harman, the local MP, said people were asking questions about fire escape routes. She said: "There will have to be a thorough investigation."

Zahera Chaudry, 21, whose sister was in a first-floor flat when the blaze broke out, said: "These buildings should have been torn down years ago." She said there was no central fire alarm system in operation but some of the individual flats were fitted with alarms.

Assistant Commissioner Nick Collins, of the London Fire Brigade, said it was "one of the most significant fires in some time in terms of lives lost". He said the block's construction was "common" in the capital but the blaze's rapid spread unusual.

Ian Wingfield, a local Labour councillor and the party's spokesperson for public housing in the borough, called for a full public investigation into such blocks across the country.

Nick Stanton, the leader of Southwark Council, issued a statement yesterday, saying: "We are as anxious as anyone to understand how this fire started and took hold of this block. We will give our full support to the thorough investigation and will assist it in every way we can."