The council has been widely criticised for its handling of the disaster, with residents complaining that officials had provided little support or information. Gold Command, a hierarchy to organise the emergency response, will now be led by a group of chief executives from councils across London. It has also been renamed the Grenfell Fire Response Team.
"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, suggesting that contractors might be destroying evidence before it is sought by police.
Speculation has focused on the role that may have been played by the cladding since the fire tore through the 24-story Grenfell Tower in the early hours of Wednesday, leaving at least 58 people presumed dead.
Commander Stuart Cundy of the Metropolitan Police warned that the death toll could rise further as authorities continue to search the wreckage.
Labour leader Jeremy Corbyn has already called on the government to conduct an investigation into reports that Gavin Barwell, the former housing minister who was recently appointed as the Prime Minister's adviser, had failed to OK a fire safety review request he had received.
He told ITV: "Occupy it, compulsory purchase it, requisition it - there's a lot of things you can do".
The tragedy has laid bare divisions in a London borough where extraordinary wealth exists in proximity to public housing estates, and brought scrutiny to a local council long dominated by the Conservatives.
Volunteers and community organisers involved in the Grenfell response have repeatedly voiced frustration at the lack of official support from the council and the central government. We're sitting on almost £300 million [€342 million].
"When an existing building is undergoing a renovation, upgraded fire safety measures may be required depending on the type of insulation and cladding proposed as part of the renovation", he said.
Theresa May offers support package for London fire victims
But the identification of the victims appears to be proving very hard , which experts attribute to the extreme heat of the fire. Cundy added that it will take weeks or longer to recover and identify all the dead in the housing block that was devastated.
But Mr Paget-Brown said: "There's an effective, coordinated relief effort on the ground and I'm sorry if people haven't seen that".
Linda Wade, a Liberal Democrat councillor, said: "The communication has been appalling". Honour to stand alongside the community to pray for the victims of the #GrenfellTower fire.
Public anger boiled over on Friday afternoon, with hundreds of protesters occupying the council building.
Meanwhile, a company involved in the renovation of the tower was forced to deny cladding on the building was banned in the United Kingdom after comments made by Chancellor Philip Hammond.
London Mayor Sadiq Khan has attended a church service near the ruined London high-rise apartment building where at least 58 people perished.
The refurb also didn't include any sprinklers, but Hammond claimed they weren't necessarily needed to ensure other tall buildings in the country don't go up in flames.
"If the conclusion of a proper technical evaluation is that [fitting sprinklers] is the best way to deal with the problem, then of course".
Cladding used on Grenfell Tower blamed for spreading the London blaze is banned in Britain, Finance Minister Philip Hammond says.
The type of plastic-filled exterior cladding implicated in the rapid spread of the deadly London tower fire is permitted in Ontario on buildings under seven storeys.