So far, 58 people have been feared dead - a toll that authorities warn could rise ahead of new figures to be released on Monday.
The cause of Wednesday's blaze is still under investigation, but anger has mounted in the community amid reports that exterior paneling used in an extensive renovation completed past year may have spread the flames.
Metropolitan Police Stuard Cundy said: "Sadly, our work will be ongoing for many, many weeks".
Fifty-eight people are now assumed dead from last week's inferno, including 30 confirmed fatalities and 28 others believed to have been killed, Metropolitan Police Commander Stuart Cundy said Saturday.
The death toll almost doubled from 30 to 58, and it is likely to rise even further in coming weeks.
He also said it might not be possible to identify all the victims owing to the intensity of the fire and devastation it had caused.
"When the truth comes out about this tragedy, we may find that there is blood on the hands of a number of organisations", Lammy said.
"We are grateful to the Prime Minister for listening to us and for the assurances she has given us but now we need to see real action and immediate results with centralised coordination of the relief effort with residents closely involved".
The Prime Minister will chair another meeting of the Grenfell Tower Recovery Taskforce at 11am tomorrow.
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Grenfell Tower is the only high-rise building in the Lancaster West Estate, which comprises of 900 other apartments, split into smaller low-rise blocks.
"Equally, there may be people who thankfully may have managed to escape the fire and for whatever reason have not let their family or friends or police know", he said.
Of that 79, police have identified five people.
"The response of the emergency services, NHS and the community has been heroic", she said in a statement.
He said it had been "incredibly emotional working in there".
British officials have announced a nationwide minute of silence to honor the victims on Monday morning.
In addition, British health authorities will provide long-term bereavement counselling for those who lost loved ones in the tragedy.
May also said that a public inquiry that is looking into the Grenfell Fire will report directly to her and that she has asked for daily updates from the neighbourhood to be sent to her.