He said: 'Within the community, trust in the authorities is falling through the floor and a suspicion of a cover-up is rising.
"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.
"We need urgent action now to make sure that all records and documents relating to the refurbishment and management of Grenfell Tower are protected."
Lammy added that justice can only done if all records, including emails, minutes of meetings, correspondence, safety assessments and reports - are preserved.
He said: "When the truth comes out about this tragedy we may find that there is blood on the hands of a number of organisations.
"At this stage, it is my grave concern that the families of Grenfell Tower will not get justice if documents are being quietly destroyed and shredded and emails are being deleted."
Lammy, whose friend Khadija Saye died in the fire, said police had the power to seize all documents.
However he added that Section 35 of the Public Inquiry Act, which makes the destruction of any documents a criminal offence, does not apply until a chairman is appointed to an inquiry and the terms of reference set.
Harley Facades, which was paid £2.6million ($4.5 million) to supply and fit the cladding, said it had removed the Grenfell Tower page from its website "as a mark of respect".
The plastic panels - that even the manufacturer warned were a deadly fire risk - are banned on high-rise buildings in Britain, ministers said yesterday.
Director of Public Prosecutions Alison Saunders confirmed there was a criminal investigation into the fire that killed at least 58 in the early hours of Wednesday.
Former DPP and Labour MP Sir Keir Starmer told BBC1's Andrew Marr Show: "I spoke to the DPP yesterday and there are prosecutors already in, advising the police.
"There are wider regulatory offences, but I think manslaughter is the most serious and that's the one that needs to be looked at first."
Chancellor Philip Hammond said the probe would look at whether regulations had been breached at the tower in North Kensington.