"This is an unprecedented incident", London Fire Commissioner Dany Cotton told reporters Wednesday night.
He said: "We investigate criminal matters".
The Labour leader said he was "very concerned" that the probe is not used to "delay any parallel actions which might be taken by interested parties".
In addition to those killed, the blaze injured at least 74 people.
Some people then left the building though others remained inside.
The fire forced residents to flee through black smoke down the single stairwell, jump out of windows or even drop their children from the 120-apartment building.
The commander said video and photographs from inside the "considerably damaged" 24-storey tower are going to be released on Sunday.
"We are in the richest borough in the United Kingdom and in this very borough we have a building where some of the poorest live and the safety measures are totally inadequate", said Mustafa Al Mansur, one of the organisers of the demonstration.
He added: "What did she bring, what useful things did she bring?"
Fifty-eight people are missing and presumed dead in the Grenfell Tower disaster, the officer in charge of the investigation said.
"We need to know what commitment the council is taking to ensure this tragedy is not repeated", he said.
Protesters in London accused authorities of suppressing the true death toll, an idea that has spread on social media.
No further survivors are expected to be found and criticism continues to mount for Prime Minister Theresa May's response to the tragedy.
Downing Street also announced a £5 million fund for emergency supplies, food and clothing.
The package includes a guarantee to rehouse people as close as practically possible to where they previously lived, either in the borough of Kensington and Chelsea or in neighbouring boroughs.
The local Grenfell Action Group had claimed, before and during a major 10-million-pound refurbishment of Grenfell Tower previous year, that the block constituted a fire risk and residents had warned that access to the site for emergency vehicles was "severely restricted".
Tower block blaze: What we know
Residents rushed to escape through smoke-filled corridors in the housing block after being woken up by the smell of burning. I looked out my window, I leaned over and I could see the fire blazing up. "I'm anxious about my building now", she said.