“I looked out of the window, and the flames were rising up the building,” Ms. Wahabi, of the ninth floor, said a few hours after she had escaped. “The flames were unbelievable. Pieces of the exterior were breaking off. Cladding was flying through the air.”

Ms. Wahabi said that she had spoken by telephone with her brother, who was on the 21st floor, and urged him to leave, but that he had been told by firefighters to stay in place until he could be rescued.

She said she had not been able to contact him since, adding, “I have done a lot of crying.”

The building was populated by many immigrants, from countries that included Eritrea, the Philippines, Somalia and Sudan. Many were observing Ramadan and preparing or eating suhoor, the predawn meal.

Among them was Mr. Abbas, who was visiting his cousin.

“I opened the door and everyone was shouting, ‘Fire, fire, get back in,’ ” he recalled. “Then a neighbor called my cousin and told us to wait for the Fire Brigade. We were terrified and thought about trying to get out the window. There were people dangling out the windows trying to get out.”

He added: “My cousin had his kids with him, and they started crying and screaming when the smoke started coming in. There was no way out, we were stuck, and no one was coming to help us.”

“I don’t know how long it took, but it felt like ages before we got out,” Mr. Abbas said. “I could see people lying on the floor as we were being pulled out. I think a lot of people died. It’s a nightmare.”

Abdul Kadiri, who lives nearby, was reunited with a friend who lived on the 15th floor of Grenfell Tower, and who called Mr. Kadiri as flames licked the building. “I told him to grab his family and get out, and he hung up,” Mr. Kadiri recalled.

Another neighborhood resident, Alison Evans, woke to the sound of sirens and helicopters and watched flames engulf the building from a nearby street. “It just kept burning and burning for hours, and for hours there were still people at the top of the building screaming for help,” she said. “It was hell to watch.”

Another resident, Mohammed Bouya, said he could hear people screaming for help from their windows. Firefighters told them to stay where they were, he said.

The so-called stay-put policy is not uncommon for British high-rises, but the resident association had complained about it, saying that it would hinder escape in the event of a fire. Nonetheless, the management company had recently posted fire safety instructions — including the stay-put policy — at the building’s entrance and outside elevators on every floor.

The intensity and power of the fire led to fears that the building might collapse, but rescue workers and investigators were able to enter after the flames had been beaten back.

Donations of food, water, clothing, diapers and toiletries poured in to the reception centers, including the Rugby Portobello Trust, a charity, where the volume of items — including pillows and a cooling fan — was so great that volunteers had to place them in boxes on the sidewalk to take to other locations. A gym opened its showers for displaced residents, and the Westway Sports and Fitness Center provided mattresses.