Mr Magee revealed 999 operators dealt with up to 172 fire survival guidance calls, when a trapped person can not leave their home and stays on the line.
At least 30 people are now confirmed to have died in the Grenfell Tower fire, police have said.
The protesters chanted: "We want justice", "bring them out" and "shame on you".
Fire engulfed the social housing block, where as many as 600 people lived in more than 120 apartments, in the early hours of Wednesday, turning it into a flaming torch in minutes.
Britain's Press Association reported that some 70 people were missing after compiling a list of verified reports.
"They probably had some hope that when they saw the fire brigade down there that we would get in and help them".
Theresa May's most senior minister has said critics of her handling of the Grenfell Tower tragedy are being "terribly unfair".
After two days in which her government has struggled to respond to the devastating fire at Grenfell Tower, west London, May met survivors privately on Friday and promised a series of aid measures, including 5 million pounds ($6.4 million) for emergency costs and a promise to find homes nearby within three weeks.
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.
Ms May says the fund aims to "give the victims the immediate support they need to care for themselves and for loved ones".
There were chaotic scenes as angry protesters shouted through a loudspeaker.
Police said on Friday that they had identified the place where the fire originated, and disclosed that it was unlikely to have been started deliberately.
"We can't afford to wait many years for those answers, which is why I am today calling for an interim report to be published this summer".
The west London borough of Kensington and Chelsea ranks among the wealthiest areas in the United Kingdom, but also includes pockets that are among the most deprived, including the area around Grenfell Tower.
Some residents had warned months ago that the tower represented a risky fire risk.
The Times reported that contractors are thought to have used panels with a polyethylene core for the Grenfell project.
Building and Construction Minister Nick Smith said the building code was amended in January to restrict the use of combustible cladding in buildings after fires in Melbourne and Dubai.
Jonathan Lum, an advertising executive who lives on the 57th floor of a glittering Manhattan tower designed by Frank Gehry, said if a fire breaks out there, he will heed the wisdom of the fire department and stay in his apartment, but partly because he lives in a building constructed in the past decade. It did not address the exact makeup of the panels.
Areas near the blaze are covered in posters showing missing persons.
The death toll is expected to rise further as rescue workers continue to search for victims - an operation that Metropolitan Police Commander Stuart Cundy described as "extremely challenging".
Overnight, 109 families made homeless from the blaze were housed at hotels in west London.
Numerous displaced are living in churches and community centers.
One message said: 'Fire hoses taken out, no fire alarms, no sprinklers, key fobs not working, no fire exists. "Sometimes all that's left is ash".
He said the "exceptionally complex" investigation would take several months, and there would be no room for "plodding bureaucracy" in the official response. "I will help you from up there".
Even amid the chaos and the frustration, some found a moment to seek unity.
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