As she spoke to Sky News at the site of the fire in west London, Ms Leadsom was confronted by a local resident, who said opportunities had been missed to make the 24-storey block safe following a report into the 2009 Lakanal House fire in Camberwell, south London.
Officials on Friday increased the death toll from 17 to 30, with numerous missing still unaccounted for.
The 24-story Grenfell Tower in the north Kensington neighbourhood in west London is near several major transport hubs.
As firefighters keep searching the charred ruins of the Grenfell Tower public housing complex with sniffer dogs and drones, Cundy said there was “a risk that, sadly, we may not be able to identify everybody”.
It later issued a new statement, removing the previous mention of the building meeting fire regulation standards, instead saying the project met “all required building regulations”.
The area surrounding the tower has been plastered by desperate relatives with pictures of the missing, from grandparents to young children.
Queen Elizabeth, 91, and her grandson Prince William also visited residents and emergency workers on Friday.
Asked if she had misread the public anger, she replied: “What I have done since this incident took place is, first of all, yesterday ensure that the public services had the support they need in order to be able to do the job they were doing in the immediate aftermath”.
The fire, which started just before 1 a.m. Wednesday, surprised many as they slept and the speed with which it spread shocked fire experts. Officials warn that no further survivors are likely to be found.
Jim Fitzpatrick, an MP with the main opposition Labour Party, slammed the Conservative-led government for shuffling its feet on the review. “I’ve come here today because I wanted to meet residents”. Three are in critical condition.
May met victims privately at a central London hospital on Friday and had expressed her sorrow on television on Thursday after meeting emergency services personnel.
The move came after strong criticism from London’s mayor, Sadiq Khan.
Firefighters searching the smoldering ruin in west London have recovered six bodies from the 24-story Grenfell Tower, while 11 others have been located but can not yet be removed from the gutted structure.
There were many chants of “Not 17” – a reference to the fact that they believe many more than 17 have died in the fire.
In November, the Grenfell Action Group highlighted ongoing concerns among residents over the safety of the tower, managed by the Kensington and Chelsea Tenant Management Organisation on behalf of the borough.
“Mohammed undertook a risky journey to flee war and death in Syria, only to meet it here in the United Kingdom, in his own home”, the Syrian Solidarity Campaign said in a statement.
The Syria Solidarity Campaign said Alhajali, a civil engineering student, had been in a flat on the 14th floor when the fire broke out, and had spent two hours on the phone to a friend in Syria. The police chief said the figure of 58 included that toll given earlier.
An £8.6m refurbishment – part of a wider transformation of the estate – was completed by Rydon Construction in May previous year. It had a plastic core and was similar to that used by high-rise buildings in France, the United Arab Emirates and Australia which had also suffered fires that spread.
A woman touches a missing poster for 12-year-old Jessica Urbano on a tribute wall after laying flowers on the side of Latymer Community Church next to the fire-gutted Grenfell Tower in London, Friday, June 16, 2017, after a fire.
Anger swelled, meanwhile, as survivors and others pressed for answers on whether inadequate safety systems or substandard construction material could have contributed to the blaze.