The 24-story Grenfell Tower in the north Kensington neighborhood in west London is near several major transport hubs.
Police said Saturday that 30 people had been confirmed dead since the fire, while another 28 remain missing and are presumed dead.
'Family liaison officers are supporting families, and that includes those people we know to be dead; some of those who are critically ill and sadly those people who we have been told were in Grenfell Tower that night who we have been unable to trace.
Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people "if there is evidence".
He said: "I think she reassured them, that to some extent, by underlining that concerns about the numbers that police were going to be asked to give realistic assessments rather than just figures".
It said: "We are devastated by this tragedy".
"Khan went on to call Wednesday's massive Grenfell Tower fire "a preventable accident that didn't need to happen" - and said the tragedy was "a outcome of the mistakes and neglect from politicians from the council and from the government".
Writing in the Observer on Sunday, Mr Khan suggested high-rise tower blocks dating from the 1960s and 1970s could be torn down in the wake of the fire, which he said may well be the "defining outcome of this tragedy".
NHS England says the injured are being treated in four London hospitals.
Cundy said authorities plan to release video and photographs from inside the badly-charred building.
Police have been struggling to come up with an authoritative list of who was in the building when the fire started, making it hard to determine how many had died.
British Prime Minister Theresa May, facing criticism for the government's handling of the disaster, met Saturday with 15 fire survivors invited to her official residence at 10 Downing Street.
Labour Party leader Jeremy Corbyn said Sunday the government has the power to take over empty apartments and offer them to the hundreds of Grenfell Tower residents left homeless in Wednesday' inferno.
"Four hundred or so people - still majority have not got somewhere decent or safe or secure to stay", he said.
"I've heard stories of heroism, from Christians, from Muslims and from others, looking after their brothers and sisters, their neighbours and doing the job that we expect from this brilliant community because of the fantastic community that is here in this part of London".
Officials are using dental records, fingerprints and DNA samples to try and positively identify victims.
Earlier on Saturday, Queen Elizabeth II and Prince Philip observed a moment of silence to honor the victims.
Khan is London's first Muslim mayor. The queen said it was "difficult to escape a very somber mood" on what is normally a day of celebration. "Wherever we can, we will bring people to justice if there is evidence". Survivors of the building claim that cheap materials for the cladding and a lack of maintenance on the building were to blame for the fatal fire.
The company that installed the cladding, Harley Facades Limited, said in a statement Wednesday that it was "not aware of any link between the fire and the exterior cladding to the tower". Clement's Church, also close by, and that it was an honor to stand alongside the community to pray for the fire victims.