LONDON—Police on Saturday identified five of the six people killed when fire swept through a London high-rise, as investigators try to find out what started the blaze and whether the building’s design contributed to the tragedy.

Police said the victims were Helen Udoaka, 34, and her 3-week-old daughter Michelle; Dayana Francisquini, 26; 3-year-old Filipe Francisquini; and Catherine Hickman, 31. The sixth victim has not been named.

Chief Superintendent Wayne Chance of the Metropolitan Police said the fire started on the ninth floor of the 12-story building, which has about 100 apartments. The victims were all on the 11th floor.

He said police were treating the building as a crime scene and the fire as suspicious because they did not yet know the cause.

London Mayor Boris Johnson said officials wanted to know “whether there was any suspicion, whether there was any arson, whether the fire was set, whether there was any malign intent, and 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.”

Many residents escaped down the building’s stairs, but 30 had to be rescued by firefighters.

“The people were in the windows, screaming out for help,” said Lincent Johnson, 28, who lives across the street.

One piece of video footage showed three people, including a baby, sheltering on a balcony as smoke swirled around them.

Residents said the 1960s building, part of a large public housing estate, had recently been refurbished, with new windows and electrical wiring. But some complained that the layout, with just a single central staircase, was dangerous.