Theresa May, Britain's embattled Prime Minister, is facing criticism for failing to meet residents when she visited the scene Thursday.
The tragedy has provoked a huge response from nearby communities.
The 23-year-old Alhajali is the only victim of the Grenfell Tower fire to be officially named as the hard process of identifying human remains continues.
Dozens of people have been reported missing since last Wednesday's early-morning blaze that struck while many who live in the building's 120 apartments were asleep.
"It is so important to me that the families have every confidence in our identification procedure and processes so they know it is their loved ones being returned to them and that is why it is so exhaustive", Cundy added.
Police Commander Stuart Cundy said the number of 58, which was based on reports from the public, may rise and includes the 30 deaths that have already been confirmed.
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.
"We do not want another fatality arising out of this tragedy".
When asked about the search, he replied that the officers had gone "all the way to the top" of the tower, and explained that the first phase was a visual search.
"That is also an absolute priority for the investigation - to establish who they may be".
He also appealed to anyone who may have escaped from the building, but has not yet come forward, to make themselves known.
He said the group had spoken about their "demands and what we expect".
Mrs May said she had fixed a deadline of three weeks for everybody affected to be rehoused locally.
Police said they are using the INTERPOL Disaster Victim Identification Standards to identify the deceased.
"It is human nature for most of us - if we know there's a fire, start moving and get out", said Robert Solomon of the National Fire Protection Association, a USA -based organization that studies fire safety globally.
Meanwhile, the Home Office said it was making arrangements for the family of one of those who died in the fire to travel from Syria to Britain for his funeral. But I don't think anything prepared me for what I was going to see when I was in there.
Anger flared in the Kensington community over the weekend - with many protests taking place across the capital - as some accused the authorities of withholding information and responding inadequately.
Cundy said a criminal investigation began the day of the fire and will look at a "wide range" of issues, including the renovation project, the public housing block's management and maintenance, and fire-safety measures.
"They feel the government and local council haven't done enough to help them in the aftermath of this horrific incident, or to provide answers to their increasingly urgent questions", Khan wrote. The British government has announced a 5 million-pound ($6.3 million) emergency fund for the victims.
The government has promised a full public inquiry, but that has done little to ease a sense of frustration at the lack of information about how the fire moved so quickly to engulf the building.