British Prime Minister Theresa May on Saturday said that support for families in the immediate aftermath of the Grenfell Tower disaster was "not good enough". "We'll get to the bottom of this", she said.
May has come under personal attack for failing to meet residents during her first visit to the site.
Media reports have placed the number of people in the building at the time of the blaze at between 400 and 600.
Cundy said police would consider criminal prosecutions if there is evidence of wrongdoing and the police investigation would include scrutiny of the renovation project.
After a botched snap election that lost her party its majority in parliament, May is facing criticism for her response to the blaze which engulfed the 24-storey apartment block of social housing on Wednesday.
Speaking later outside Scotland Yard, Mr Cundy added: "I have investigated major crime for most of my service and I have seen some bad things". He says "my heart goes out to those affected".More news: Ex-NFL/UNC player Lawrence Taylor pleads guilty to Florida DUI
Hands and Treasury chief Philip Hammond said in separate TV appearances that the cladding used on Grenfell seems to be prohibited by British regulations.
Two Underground lines near the fire area were partially shut down on Saturday to make sure that debris did not land on the tracks.
Meanwhile, residents and families met with the Prime Minister at No.10 as Theresa May was blasted for her handling of the disaster.
The announcement by a spokesman comes a day after May was heckled during a visit to the west London neighbourhood where Wednesday's inferno took place.
Former conservative minister Michael Portillo said on Thursday that, although she had met in private with members of the the emergency services, she should have met Grenfell Tower residents, as Labour leader Jeremy Corbyn did.
In her traditional birthday message, the 91-year-old monarch made a reference to the "succession of bad tragedies", a day after she paid a visit to people affected by the massive Grenfell Tower blaze in west London. Hundreds of others have been left homeless and dozens are missing. She also said she will receive daily reports from the stricken neighborhood.
"Put to the test, the United Kingdom has been resolute in the face of adversity", Elizabeth said.More news: Warriors have LeBron, Cavs on ropes after going up 3-0
The queen's official birthday is marked in June when the weather is often nicer than in April, the actual month of her birth. Police said 19 injured in the fire remain hospitalized, including 10 who were in critical condition.
In addition to those killed, the blaze injured at least 74 people. She has also pledged $6.4 million in support to the residents and promised that those who lost their homes would be relocated within three weeks.
The government has committed £5 million for clothes, food and emergency supplies for the victims.
Speaking outside St Clement's Church, Mr Khan said: "There is a feeling from the community that they have been treated badly because some of them are poor".
Among concerns previously been raised by people in the wake of the fire was the lack of a centralised missing person list and worries over where Grenfell residents will be rehoused.
Many are demanding answers for how the blaze spread so quickly.
"All our warnings fell on deaf ears and we predicted that a catastrophe like this was inevitable", the group said after the fire broke out, according to the Associated Press.More news: Russia: US Warplanes West of Euphrates in Syria Now Legitimate Targets
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