In parallel, the police are seeking to identify if any criminal offences had been committed.
King also said that there are around 4,000 tower blocks in the United Kingdom without automatic fire sprinkler protection systems in place.
The government has set up a £5 million ($6.4 million, 5.7 million euros) emergency fund for the Grenfell Tower residents, allocating a minimum £5,500 to each household with £500 cash payments already being handed out.
There are questions about why the block was not fitted with sprinklers or a central smoke alarm, as well as whether the recent refurbishment - including the use of cladding that was blamed for worsening previous building fires in France, the United Arab Emirates and Australia - helped fuel the flames.
Ronnie King, the UK's former chief fire officer, told Al Jazeera: "I wouldn't wish to denigrate those who installed the cladding because - whatever the cladding was - it did not have to be fire resistant under the building regulations", said King.
"The prime minister needs to act immediately to ensure that all evidence is protected so that everyone culpable for what happened at Grenfell Tower is held to account and feels the full force of the law", Lammy said.
The government is struggling to find temporary housing for people who lived in the 24-story tower.
He said all records - including emails, minutes of meetings, correspondence with contractors, safety assessments, specifications and reports - must be kept intact.
"It is hard to escape a very sombre national mood", the queen said in a statement to mark her official birthday - an occasion that typically does not result in any public comments from the monarch. "I said 'why you didn't come - they brought us outside, I thought you are with us.' He said 'no one brought me outside.' He said, 'why you left me?'"
Celtics and 76ers agree on trade for No. 1 draft pick
He's giving me tips and pointers and he's pretty amusing , so when I saw that it was pretty cool and pretty amusing . And like I said, I'm close to home, so a lot of feelings could come out and just show love to the city.
Families from Grenfell Tower and local residents have in the last few days complained about the lack of support from Kensington and Chelsea council.
Mrs May has come in for a barrage of criticism over her response to the disaster, including being jeered when she visited the North Kensington estate on Friday.
Floral tributes and messages for the victims of Grenfell Tower are seen in London, Britain, on June 16, 2017.
The Home Office said late Saturday night it will make arrangements for the family of Mohammad Alhajali to "travel to the U.K.in these terribly sad circumstances".
Speaking to reporters on Friday, Cundy said: "I'm able to say at this point in time at least 30 people have died as a result of this fire".
"He came to the United Kingdom because he had ambitions and aims for his life and for his family".
The first victim to be identified was Mohammed Alhajali, a 23-year-old Syrian refugee.
London police said Saturday that the death toll from the inferno at the Grenfell Tower in west London had risen to 58.
The recovery effort resumed this afternoon, but the police warn it could take weeks for answers to emerge.
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