Labour Party lawmaker David Lammy said that the government and the police should immediately seize all documents relating to the building's renovation to prevent the destruction of evidence that could show criminal wrongdoing.
The 24-story Grenfell Tower in the north Kensington neighborhood in west London is near several major transport hubs.
The government on Saturday promised a public inquiry and police have opened a criminal investigation.
Theresa May was so moved by the stories of Grenfell victims during her meetings with them this weekend that she was "welling up", according to a reverend who was there. One, are our regulations correct, do they permit the right kind of materials and ban the wrong kind of materials?
"The second question is, were they correctly complied with".
"That will be a subject that the inquiry will look at".
"We're all desperately sad, we're all angry, but of course none of us as angry as those who were directly affected, " Green said.
Experts say the cladding and the insulation it contained seems to have spread the flames quickly along the exterior of the building, overwhelming safety devices like fire doors.
He says the search for remains had been paused because of safety concerns but has resumed.
'I must consider the fact that there may be others in the building who, for whatever reason have not been reported to us.
London mayor Sadiq Khan acknowledged growing public anger surrounding the Grenfell Tower fire in which 58 people are presumed dead, saying the blaze was a result of "mistakes and neglect". Nineteen people remained in hospital as of Saturday afternoon, of whom 10 were receiving critical care.
The tower's cladding will likely be one of only many factors taken into account as investigators probe what happened.
The government is carrying out an "urgent inspection" of roughly 2,500 similar tower blocks across the country to assess their safety.
Cundy said authorities plan to release video and photographs from inside the badly-charred building. "If something needs to be done to make buildings safe it will be done".
Nicholas Paget-Brown said there were "enormous challenges" facing his borough's residents.
At least 30 people were killed in Wednesday's inferno at the Grenfell Tower, while dozens of others are missing. Bellerin, a defender, also plays for London club Arsenal.
"Trust is very, very low". Contractors are removing Grenfell details from their websites. He says it will take weeks or longer to recover and identify all the dead in the public housing block that was devastated by a fire early Wednesday.
Police have been struggling to come up with an authoritative list of who was in the building when the fire started, making it hard to determine how many had died.
"Four hundred or so people - still a lot of them have not got somewhere decent or safe or secure to stay", he said.
"All I'm keen to say is there is an effective, co-ordinated relief effort on the ground and I'm sorry if people haven't seen that". The group left after a meeting that lasted more than two hours but did not speak to reporters gathered outside.
"During recent visits in Manchester and London, I have been profoundly struck by the immediate inclination of people throughout the country to offer comfort and support to those in desperate need", the queen said in a statement.
Flowers and posters of missing persons are still taped to the gates of the church, which has been used as a temporary shelter and gathering point for donations.