They also expressed anger that the prime minister did not meet with survivors or victims of the fire when she initially visited the neighborhood following the tragedy.
"I have heard the concerns and I have ordered immediate action across the board to help victims' relatives and the survivors", May said. May has committed five million pounds for clothes, food and emergency supplies as part of Grenfell Tower Residents' Discretionary Fund on Friday, which includes the aim to re- house residents within three weeks as close to where they lived before as possible, to pay for temporary housing in the meantime and to provide extra financial assistance.
They would wear high-visibility clothing so that they could easily be found, dispense advice and ensure the right support was provided, she added.
His call was echoed by London Mayor Sadiq Khan who wrote an open letter to Theresa May demanding that she confirm "as a matter of urgency" that everyone from Grenfell Tower and other evacuated properties "will be rehoused locally immediately".
Only one victim has been formally identified so far: 23-year-old Syrian refugee Mohammad Alhajali. However, the identification of the other victims is proving very hard - which experts attribute to the extreme heat of the fire.
The government has promised a full public inquiry.
"Wallowing in the wash of a general election that stripped our prime minister of her authority on the very eve of European Union negotiations, neither common sense nor the evidence suggest she can re-establish public confidence", Matthew Parris wrote.
Trade Minister Greg Hands added that the government is conducting what he called an "urgent inspection" of some 2,500 other tower blocks across Britain to evaluate their safety.
Many residents of the building remain unaccounted for, and police said numerous remains may never be identified.
The track in question is above ground and lies a stone's throw away from Grenfell Tower, where at least 30 people died on Wednesday after a fire engulfed the building.
At least 30 people were killed in the fire at Grenfell Tower in the west London neighbourhood of north Kensington.
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.
The Department for Communities and Local Government has said that aluminium cladding with a polyethylene core should not be used on buildings taller than 18m.
Anger flared in the Kensington community over the weekend - with many protests taking place across the capital - as some accused the authorities of withholding information and responding inadequately.
The company behind the renovation also reportedly used banned, flammable cladding on the building's exterior to cut costs and make it more aesthetically attractive for neighbors in the Kensington and Chelsea borough, one of the UK's richest areas. "We were seeking a change to the building regulations for that very goal", he added.
The venue had been a focal point for efforts to support those affected by the fire which engulfed the apartment tower in a matter of minutes. Cundy said emergency workers have now reached the top of the tower.
In the fire's aftermath, the London Underground on Saturday suspended subway service between Edgware Road and Hammersmith on two lines at the request of the London Fire Brigade.
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